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### Department of Algebra

| Seminars | History of the Department | Areas of Research | Main Results | Awards | International Relations | Publications |
Staff
 Parshin Aleksei Nikolaevich Doctor Phys.-Math. Sci., Academician of RAS, Head of Department office: 525; tel.: +7 (499) 941 01 79, +7 (495) 984 81 41 * 39 33; e-mail: parshin@mi-ras.ruPrincipal fields of research: Àlgebraic number theory and Galois theory. Algebraic geometry and n-dimensional local fields and their applications to arithmetics, geometry of manifolds, integrable systems, and quatum field theory. History of mathematics. List of publications Gorchinskiy Sergey Olegovich Doctor Phys.-Math. Sci., Senior Scientific Researcher office: 409; tel.: +7 (499) 941 01 79, +7 (495) 984 81 41 * 35 33; e-mail: gorchins@mi-ras.ruPrincipal fields of research: Algebraic geometry, arithmetic geometry, higher-dimensional adeles, K-theory, algebraic cycles. List of publications Kulikov Viktor Stepanovich Doctor Phys.-Math. Sci., Professor, Leading Scientific Rsearcher office: 524; tel.: +7 (499) 941 01 79, +7 (495) 984 81 41 * 36 70; e-mail: kulikov@mi-ras.ruPrincipal fields of research: Algebraic geometry and topology of algebraical manifolds. List of publications Nikulin Vyacheslav Valentinovich Doctor Phys.-Math. Sci., Leading Scientific Researcher e-mail: nikulin@mi-ras.ruPrincipal fields of research: Algebraic Geometry. Integer-valued quadratic forms generated by reflections in hyperbolic spaces. Automorphic forms. Lorentzian Kac-Moody algebras. List of publications Osipov Denis Vasil'evich Doctor Phys.-Math. Sci., Leading Scientific Researcher office: 540; tel.: +7 (499) 941 01 79, +7 (495) 984 81 41 * 39 32; e-mail: d_osipov@mi-ras.ruPrincipal fields of research: Algebraic geometry. Algebraical number theory. Integrable systems. List of publications Popov Vladimir Leonidovich Doctor Phys.-Math. Sci., Professor, Corresponding Member of RAS, Chief Scientific Researcher office: 524; tel.: +7 (499) 941 01 79, +7 (495) 984 81 41 * 36 70; e-mail: popovvl@mi-ras.ruPrincipal fields of research: Algebraic transformation groups. Invariant theory. Algebraic groups and their representation theory. Homogeneous spaces. Lie groups and Lie algebras. Algebro-geometric aspects of algebraic transformation group theory. Affine algebraic geometry. Automorphism groups of algebraic varieties. Discrete reflection groups. List of publications Abrashkin Viktor Aleksandrovich Doctor Phys.-Math. Sci., Out-Of-Staff Member e-mail: victor.abrashkin@durham.ac.ukPersonal page: http://maths.dur.ac.uk/~dma0va/ Principal fields of research: Galois moduli of finite group schemes. $p$-Adic representations for the Galois group of local fields. The Iwasawa theory. Theory of $p$-extensions of local and global fields. Highest theory of branching. List of publications Mikhailov Roman Valer'evich Doctor Phys.-Math. Sci., Out-Of-Staff Member e-mail: rmikhailov@mail.ruPrincipal fields of research: Group theory, topology, category theory, algebraic K-theory. List of publications Trepalin Andrey Sergeevich Scientific Researcher e-mail: trepalin@mccme.ru List of publications Tyurin Dmitry Nikolaevich Junior Researcher e-mail: dimtyurin@mail.ru Kostrikin Aleksei Ivanovich (12.02.1929 – 22.09.2000) Doctor Phys.-Math. Sci., Corresponding Member of USSR Academy of Sciences Shafarevich Igor Rostislavovich (03.06.1923 – 19.02.2017) Doctor Phys.-Math. Sci., Academician of RAS Personal page: http://www.mi-ras.ru/~shafarev Principal fields of research: Algebraic number theory. Algebraic geometry. Theory of Lie groups and Lie algebras. Commutative and associative algebras. List of publications Tyurin Andrei Nikolaevich (24.02.1940 – 27.10.2002) Doctor Phys.-Math. Sci., Corresponding Member of RAS Voronin Sergei Mikhailovich (11.03.1948 – 18.10.1997) Doctor Phys.-Math. Sci.
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Seminars
 Seminar of the Department of Algebra and of the Department of Algebraic Geometry (Shafarevich Seminar) Seminar Chairmen: A. N. Parshin; D. O. Orlov Steklov Mathematical Institute, room 540 (Gubkina 8) Seminar on Arithmetic Algebraic Geometry Seminar Chairman: A. N. Parshin Steklov Mathematical Institute, Room 540 (8 Gubkina) Arithmetic geometry seminar Seminar Chairmen: S. O. Gorchinskiy; D. V. Osipov; S. Yu. Rybakov; V. A. Vologodsky Seminar of the Department of Algebra Seminar Chairmen: I. R. Shafarevich; A. N. Parshin
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History of the Department

The Department of Algebra was created in the middle of 1930's. B. N. Delone was the first head. The list of people working at the department in the late 1930's and 1940's includes: O. Yu. Schmidt, S. A. Chunikhin, I. M. Gelfand, A. I. Malcev.

Starting from 1946 I. R. Shafarevich is working at the department, being its head from 1960 to 1995. Many people in the department are his pupils: A. I. Lapin (1950 and 1957–1969), A. I. Kostrikin (1956–2000; starting from 1977 he was also the head of the Chair of Algebra at the Moscow State University), S. P. Demushkin (1959–1975), A. B. Zhizhchenko (1959–1965), Yu. I. Manin (since 1960), A. N. Tyurin (1963–2002), V. A. Demyanenko (1967–1969), A. N. Parshin (since 1968, starting from 1995 he is the head of the department), S. Yu. Arakelov (PhD student from 1971 to 1974), V. V. Nikulin (1987–2002, out-of-staff member since 2002), V. A. Kolyvagin (1988–2004, out-of-staff member from 2004 to 2011), V. A. Abrashkin (1996–2002, out-of-staff member since 2002), Vik. S. Kulikov (PhD student from 1974 to 1977, then a member since 1997).

The following people have been working at the department: S. P. Novikov (1960–1975), F. A. Bogomolov (PhD student from 1970 to 1973, employee from 1973 to 1993, out-of-staff member until 2011), M. M. Kapranov (1986–1990), S. A. Stepanov (1987–2000), A. T. Fomenko (1998–2001).

Now the following people also work at the department: A. I. Bondal (since 1994), D. O. Orlov (since 1996), D. V. Osipov (since 1999), V. L. Popov (since 2002), D. B. Kaledin (since 2002), A. G. Kuznetsov (since 2002), R. V. Mikhailov (since 2004), V. V. Shokurov (since 2004), S. O. Gorchinskiy (since 2007), C. A. Shramov (since 2008), I. D. Shkredov (since 2010), A. I. Efimov (since 2010).

In 2009 the Department of Algebra was united with the Department of Number Theory. The following people have thus entered the department: G. I. Arkhipov, M. M. Grinenko (out-of-staff member since 2011), M. A. Korolev, V. V. Przyjalkowski, A. V. Pukhlikov, I. S. Rezvyakova.

In 2012 the Department of Algebraic Geometry was created on the base of the Department of Algebra and Number Theory. The following people are the members of the new department: D. O. Orlov (head of the department), A. I. Bondal, M. M. Grinenko, A. I. Efimov, D. B. Kaledin, A. G. Kuznetsov, V. V. Przyjalkowski, A. V. Pukhlikov, V. V. Shokurov, C. A. Shramov.

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Areas of Research

Algebraic number theory, Galois theory, Lie groups and Lie algebras, theory of algebraic groups, algebraic geometry (especially the category theory of coherent sheaves, birational geometry, invariant theory), arithmetic of algebraic varieties, algebraic and differential topology, mathematical physics, combinatorial group theory, homological algebra, representations of groups, mirror symmetry, theory of adeles.

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Main Results
1. Algebraic number theory and Galois theory
• Construction of a general reciprocity law (I. R. Shafarevich, A. I. Lapin), solution of the inverse problem of the Galois theory for solvable groups (I. R. Shafarevich).
• Description of p-extensions of local and global fields (I. R. Shafarevich, S. P.  Demushkin, H. Koch), solution of the problem of class field tower (E. S. Golod and I. R. Shafarevich), the structure of the Galois group for local fields (V. A. Abrashkin).
• Theory of Euler systems (V. A. Kolyvagin).
2. Lie groups and Lie algebras
• Semi-simple subgroups of Lie groups, nilmanifolds (A. I. Malcev).
• Theory of infinite-dimensional representations of classical Lie groups (I. M. Gelfand and M. A. Naimark).
• Solution of the weak Burnside problem for an arbitrary prime exponent (A. I. Kostrikin).
• Classification of simple Lie algebras in the positive characteristic (A. I. Kostrikin and I. R. Shafarevich).
• Integral lattices and orthogonal decompositions of Lie algebras (A. I. Kostrikin).
• Theory of Kac–Moody Lorentz algebras (V. A. Gritsenko, V. V. Nikulin).
3. Algebraic geometry
• Geometry of algebraic varieties: pencils of elliptic curves (I. R. Shafarevich), the Gauss–Manin connection (Yu. I. Manin), finiteness theorems for families of curves (A. N. Parshin and S. Yu. Arakelov).
• Theory of vector bundles: classification and Torelli type theorems for vector bundles over algebraic curves, the problem of a bundle of quadrics, vector bundles over an infinite-dimensional projective space (A. N. Tyurin).
• Theory of algebraic K3 surfaces and manifolds with a trivial canonical class: Torelli theorem (I. I. Piatetski-Shapiro, I. R. Shafarevich), structure of K3 surfaces in positive characteristic (A. N. Rudakov, I. R. Shafarevich), group of automorphisms, topological classification (V. V. Nikulin), surjectivity of the period map (V. S. Kulikov), classification of complex manifolds with trivial canonical class (F. A. Bogomolov).
• Solution of three-dimensional Lüroth problem (V. A. Iskovskikh, Yu. I. Manin).
• Flat and projective structures on Riemann surfaces (A. N. Tyurin).
• Theory of stable vector bundles on algebraic varieties (F. A. Bogomolov).
• Arithmetic groups in hyperbolic spaces and integral lattices (V. V. Nikulin).
• Smooth invariants of algebraic surfaces (V. Y. Pidstrigach, A. N. Tyurin).
• Derived categories of coherent sheaves on algebraic varieties and equivalences between them for varieties with ample and anti-ample canonical class, as well as for abelian varieties (M. M. Kapranov, A. I. Bondal, D. O. Orlov).
• Derived categories of coherent sheaves on a symplectic resolution of an arbitrary singularity (D. B. Kaledin).
• Theorem on integral kernel for an equivalence between derived categories of coherent sheaves on possibly singular projective varieties (D. O. Orlov, V. A. Lunts).
• Theory of homological projective duality (A. Kuznetsov).
• Derived categories of coherent sheaves on isotropic Grassmannians (A. G. Kuznetsov, A. E. Polishchuk).
• Prym varieties, their difference with Jacobians, and applications to the three-dimensional birational geometry (V. V. Shokurov).
• Minimal model program and its applications to higher-dimensional geometry. Moduli of polarized log pairs and positivity of the module part in the adjunction formula (V. V. Shokurov).
• Application of unramified Brauer group to the unirationality problem for algebraic varieties (F. A. Bogomolov).
• Topology of algebraic surfaces: Chisini conjecture for generic projections of algebraic surfaces onto projective plane, counterexamples in deformation theory, description of components of the Hurwitz spaces of coverings of algebraic curves (Vik. S. Kulikov).
• Birational geometry of Fano varieties: description of the structures of a rationally connected fibration on Fano double spaces of index 2 and dimension 5 and above, computation of the group of birational automorphisms and the proof of non-rationality (A. V. Pukhlikov).
• Invariant theory: algebraic groups as groups of automorphisms of algebras, solution of the problem of rationality of the function field on a connected semisimple algebraic group over the subfield of central functions, description of Cayley groups (V. L. Popov).
• Applications of algebraic geometry and Tannakian categories to the differential Galois theory, parametrized Picard–Vessiot extensions (S. O. Gorchinskiy, A. I. Ovchinnikov).
• Deformation quantization of algebraic varieties over a field of positive characteristic. Noncommutative analogues of the Cartier morphism and the Frobenius map for cyclic homology (D. B. Kaledin).
4. Arithmetic of algebraic varieties
• Diophantine equations of degree three (B. N. Delone and D. K. Faddeev).
• Arithmetic of elliptic curves and abelian varieties: theory of principal homogeneous spaces (I. R. Shafarevich), unboundedness of rank over function fields (A. I. Lapin), boundedness of p-torsion of elliptic curves (Yu. I. Manin), estimates for the torsion of elliptic curves (V. A. Demyanenko), canonical heights of abelian varieties (A. N. Parshin), l-adic representations of Galois groups associated with abelian varieties, the group of points of finite order (F. A. Bogomolov), proof of the nonexistence of smooth abelian schemes over Z (V. A. Abrashkin).
• Finiteness theorems in Diophantine geometry: proof of the Mordell conjecture on rational points over function fields (Yu. I. Manin), method of ramified coverings (A. N. Parshin), finiteness of the Tate–Shafarevich group for modular curves (V. A. Kolyvagin).
• Arithmetic surfaces (Arakelov geometry).
• Arithmetic of rational and cubic surfaces (Yu. I. Manin, V. A. Iskovskikh).
• Theory of p-adic L-functions and modular forms (Yu. I. Manin).
• Theory of n-dimensional local fields and its applications to class field theory, vector bundles and the theory of algebraic groups (A. N. Parshin).
• Theory of adeles: measure theory and harmonic analysis on adelic spaces of two-dimensional schemes (D. V. Osipov, A. N. Parshin), symbols and reciprocity laws (D. V. Osipov), adelic resolutions for sheaves (S. O. Gorchinskiy, D. V. Osipov).
5. Algebraic and differential topology
• Theory of cohomological operations. Description of complex cobordisms. Classification of simply connected smooth manifolds of dimension ≷ 4. Proof of topological invariance of Pontryagin classes. Theory of foliations on smooth manifolds. Foundations of Hermitian K-theory (S. P. Novikov).
• Theory of derived functors for non-additive functors (R. V. Mikhailov, L. Breen).
• Functorial methods in the unstable homotopy theory (R. V. Mikhailov).
6. Mathematical physics
• Solution of the periodic problem for the KdV equation by methods of algebraic geometry (S. P. Novikov).
• Classification of instantons (V. G. Drinfeld, Yu. I. Manin).
• Models of classical field theory: supergeometry, the Yang–Mills theory, and string theory (Yu. I. Manin, M. M. Kapranov).
• Description of instantons on noncommutative spaces and noncommutative twistor transform (A. Kapustin, A. G. Kuznetsov, D. O. Orlov).
• Homological mirror symmetry and the category of D-branes for Landau–Ginzburg models (D. O. Orlov). Homological mirror symmetry for curves of genus greater than one (A. I. Efimov) and del Pezzo surfaces (D. O. Orlov).
7. Combinatorial group theory and applications
• Theory of central series for groups (R. V. Mikhailov).
• Description of homotopy groups of spheres in terms of group theory (R. V. Mikhailov, J. Wu).
8. Representation theory
• Moduli space of representations of Lie algebras in positive characteristic (I. R. Shafarevich, A. N. Rudakov).
• Classification and character theory for irreducible representations with finite weight of discrete Heisenberg groups (A. N. Parshin, S. A. Arnal).
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Awards

Among the members of the department there are recipients of the Fields Medal (S. P. Novikov), the Lenin Prize (I. R. Shafarevich, Yu. I. Manin, S. P. Novikov), the State USSR Prize (A. I. Kostrikin, S. A. Stepanov), the Lomonosov Prize (A. I. Kostrikin), the Alexander von Humboldt Prize (A. N. Parshin), the European Mathematical Society Prize (A. G. Kuznetsov), Russian Federation President Prize in Science and Innovation for Young Scientists (A. G. Kuznetsov) and others.

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International Relations
Department members have been repeatedly invited to the International Congresses of Mathematicians as speakers:
I. R. Shafarevich (Stokholm, 1962; Nice, 1970),
A. I. Kostrikin (Stokholm, 1962; Nice, 1970),
S. P. Novikov (Stokholm, 1962; Moscow, 1966; Nice, 1970),
Yu. I. Manin (Stokholm, 1962; Nice, 1970; Helsinki, 1978; Berkeley, 1986),
A. N. Parshin (Nice, 1970),
S. Yu. Arakelov (Vancouver, 1974),
F. A. Bogomolov (Helsinki, 1978),
V. V. Nikulin (Berkeley, 1986),
V. L. Popov (Berkeley, 1986),
V. A. Kolyvagin (Kioto, 1990),
A. I. Bondal (Pekin, 2002),
D. O. Orlov (Pekin, 2002),
 1. V. V. Nikulin, “Classification of degenerations and Picard lattices of Kahlerian K3 surfaces with symplectic automorphism group D_6”, Izv. RAN. Ser. Mat. (to appear) 2019 2. V. V. Nikulin, Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Tr. Mat. Inst. Steklova, 307, Steklov Mathematical Institute of RAS, Moscow, 2019 (to appear) 3. A. B. Zheglov, D. V. Osipov, “Lax pairs for linear Hamiltonian systems”, Siberian Mathematical Journal, 2019 (to appear) , arXiv: 1901.11130 4. Vik. S. Kulikov, Izv. RAN. Ser. Mat. (to appear) 2019 5. Vik. S. Kulikov, “On germs of finite morphisms of smooth surfaces”, Algebra, number theory, and algebraic geometry, Collected papers. Dedicated to the memory of Academician Igor Rostislavovich Shafarevich, Tr. Mat. Inst. Steklova, 307, Steklov Mathematical Institute of RAS, Moscow, 2019 (to appear) 6. V. L. Popov, “Three plots about the Cremona groups”, Izv. RAN. Ser. Mat., 2019 (to appear) , arXiv: 1810.00824 7. Vladimir L. Popov, Variations on the theme of Zariski's Cancellation Problem, 2019 , 15 pp., arXiv: 1901.07030 8. Vladimir L. Popov, “On conjugacy of stabilizers of reductive group actions”, Mathematical Notes, 105:4 (2019), 580–581 , arXiv: 1901.10858 9. V. L. Popov, “Orbit closures of the Witt group actions”, Proc. Steklov Inst. Math., 307, 2019 (to appear) 10. V. L. Popov, “Rational differential forms on the variety of flexes of plane cubics”, Uspekhi Mat. Nauk (to appear) 2019 11. S. O. Ivanov, R. V. Mikhailov, V. A. Sosnilo, “Vysshie kopredely, proizvodnye funktory i kogomologii”, Matem. sb., 210:9 (2019) (to appear) 2018 12. V. V. Nikulin, “Classification of Picard lattices of K3 surfaces”, Izv. Math., 82:4 (2018), 752–816             (cited: 1) 13. Valery Gritsenko, Viacheslav V. Nikulin, “Lorentzian Kac–Moody algebras with Weyl groups of 2-reflections”, Proceedings of London Mathematical Society, 116:3 (2018), 485–533   (cited: 1)       (cited: 1) 14. Viacheslav V. Nikulin, Classification of degenerations and Picard lattices of Kahlerian K3 surfaces with small finite symplectic automorphism groups, 2018 , 39 pp., arXiv: 1804.00991 2019 15. D. V. Osipov, “Adelic quotient group for algebraic surfaces”, St. Petersburg Mathematical Journal, 30 (2019), 111-122 , arXiv: 1706.09826 2018 16. D. V. Osipov, “Arithmetic surfaces and adelic quotient groups”, Izv. Math., 82:4 (2018), 817-836 , arXiv: 1801.02282             (cited: 1) 17. A. B. Zheglov, D. V. Osipov, “On first integrals of linear Hamiltonian systems”, Dokl. Math., 98:3 (2018), 616–618 18. Vik. S. Kulikov, “On divisors of small canonical degree on Godeaux surfaces”, Sb. Math., 209:8 (2018), 1155–1163             (cited: 1)     (cited: 1) 19. Vik. S. Kulikov, On the variety of the inflection points of plane cubic curves, 2018 , 27 pp., arXiv: 1810.01705 20. Vik. S. Kulikov, On the almost generic covers of the projective plane, 2018 , 13 pp., arXiv: 1812.01313 21. Vladimir L. Popov, “The Jordan property for Lie groups and automorphism groups of complex spaces”, Math. Notes, 103:5 (2018), 811–819 22. Vladimir L. Popov, Yuri G. Zarhin, Root systems in number fields, 2018 , 15 pp., arXiv: 1808.01136 23. Vladimir L. Popov, Three plots about the Cremona groups, 2018 , 27 pp., arXiv: 1810.00824 24. Victor G. Kac, Vladimir L. Popov, Editors, Lie Groups, Geometry, and Representation Theory. A Tribute to the Life and Work of Bertram Kostant, Series ISSN 0743-1643, ISBN 978-3-030-02191-7, Progress in Mathematics, 326, First Edition, Birkhäuser Basel (Copyright Holder: Springer Nature Switzerland AG), Basel, 2018 , X, 538 pp. www.springer.com/us/book/9783030021900 25. Vladimir L. Popov, Yuri G. Zarhin, Root symstems in number fields, Preprint MPIM 18-38, Max-Planck-Institut für Mathematik, Bonn, 2018 , 19 pp. www.mpim-bonn.mpg.de/preblob/5898 26. Vladimir L. Popov, “Modality of representations, and packets for $\theta$-groups”, Lie Groups, Geometry, and Representation Theory. A Tribute to the Life and Work of Bertram Kostant, Prog. Math., 326, Birkhäuser Basel (Copyright Holder: Springer Nature Switzerland AG), Basel, 2018, 459–479 , arXiv: 1707.07720 27. V. L. Popov, “Compressible finite groups of birational automorphisms”, Dokl. Math., 98:2 (2018), 413–415 28. V. L. Popov, Yu. G. Zarhin, “Types of root systems in number fields”, Dokl. Math., 98:3 (2018), 600–602 29. A. N. Parshin, Vestnik RAN, 88:11 (2018), 982–984 30. S. Gorchinskiy, V. Guletskiǐ, “Positive model structures for abstract symmetric spectra”, Appl. Categ. Struct., 26:1 (2018), 29–46 , arXiv: 1108.3509v3         (cited: 1)   (cited: 2) 31. S. O. Gorchinskiy, D. M. Krekov, “An explicit formula for the norm in the theory of fields of norms”, Russian Math. Surveys, 73:2 (2018), 369–371 32. S. O. Gorchinskiy, D. N. Tyurin, “Relative Milnor $K$-groups and differential forms of split nilpotent extensions”, Izv. Math., 82:5 (2018), 880–913 33. S.Gorchinskiy, C.Shramov, Unramified Brauer group and its applications, Translations of Mathematical Monographs, 246, American Mathematical Society, Providence, 2018 , xvii+179 pp. 34. S.O.Gorchinskii, K.A.Shramov, Nerazvetvlennaya gruppa Brauera i ee prilozheniya, MTsNMO, Moskva, 2018 , 200 pp. 35. Andrey Trepalin, “Quotients of del Pezzo surfaces of high degree”, Transactions of the American Mathematical Society, 370:9 (2018), 6097–6124 , arXiv: https://arxiv.org/abs/1312.6904 36. Andrey Trepalin, “Quotients of del Pezzo surfaces of degree $2$”, Moscow Mathematical Journal, 18:3 (2018), 557–597 , arXiv: https://arxiv.org/abs/1709.02006 2017 37. Valery Gritsenko, Viacheslav V. Nikulin, Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras, 2017 , 15 pp., arXiv: 1702.07551 38. V. V. Nikulin, “Degenerations of Kählerian K3 surfaces with finite symplectic automorphism groups. III”, Izv. Math., 81:5 (2017), 985–1029             (cited: 1)     (cited: 1) 39. Viacheslav V. Nikulin, Classification of Picard lattices of K3 surfaces, 2017 , 68 pp., arXiv: 1707.05677 40. V. A. Gritsenko, V. V. Nikulin, “Examples of lattice-polarized K3 surfaces with automorphic discriminant, and Lorentzian Kac–Moody algebras”, Trans. Moscow Math. Soc., 78 (2017), 75–83 41. Denis V. Osipov, “Second Chern numbers of vector bundles and higher adeles”, Bull. Korean Math. Soc., 54:5 (2017), 1699–1718 , arXiv: 1706.07354         (cited: 2)   (cited: 2) 42. Vik. S. Kulikov, E. I. Shustin, “On $G$-Rigid Surfaces”, Proc. Steklov Inst. Math., 298 (2017), 133–151           (cited: 3)     (cited: 2) 43. Vik. S. Kulikov, “The Hesse curve of a Lefschetz pencil of plane curves”, Russian Math. Surveys, 72:3 (2017), 574–576 44. Victor Abrashkin, “Groups of automorphisms of local fields of period $p^M$ and nilpotent class \$