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Tankeev, Sergey Gennadievich

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Total publications: 44
Scientific articles: 44
Presentations: 1

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Tankeev, Sergey Gennadievich
Professor
Doctor of physico-mathematical sciences (1985)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 28.02.1947
E-mail:
Keywords: algebraic cycles, Brauer groups, $l$-adic representations, conjectures of Hodge, Tate, Mumford–Tate, the Grothendieck standard conjecture (of Lefschetz type), the Friedlander–Mazur conjecture, arithmetic model, K3 surface, Enriques surface, Kalabi–Yau variety, hyperkahler variety.
UDC: 513.6, 512.6, 512.7
MSC: 14J20, 14K05, 14C30

Subject:

The Hodge conjecture is proved for all simple abelian varieties of prime dimension. The microweight conjecture holds for the $l$-adic representation associated to the Tate module of abelian variety over a number field. The finiteness of the Brauer group holds for an arithmetic model of a hyperkahler variety with the second Betti number greater than 3 over a number field. For all smooth complex 3-dimensional projective varieties of non-basic type the Grothendieck standard conjecture (of Lefschetz type) on algebraicity of the Hodge operator star is true.

Biography

Graduated from A.N. Kolmogorov's physico-mathematical boarding-school (1965). Graduated from Faculty of Mathematics and Mechanics of M.V. Lomonosov Moscow State University (MSU) in 1970 (department of algebra). Ph.D. thesis (MSU) was defended in 1973. D.Sci. thesis (MSU) was defended in 1985.

   
Main publications:
  • Tankeev S.G., Cycles on simple abelian varieties of prime dimension, Math. USSR-Izv., 20:1 (1983), 157-171.
  • Tankeev S.G., On weights of $l$-adic representation and arithmetic of Frobenius eigenvalues, Russian Acad. Sci. Izv. Math., 63:1 (1999), 181-218.
  • Tankeev S.G., On the standard conjecture of Lefschetz type for complex projective 3-dimensional varieties. II , Izv. Math. 75:5 (2011), 1047-1062.
  • Tankeev S.G., On the Brauer group of an arithmetic model of a hyperkahler variety over a number field, Izv. Math.79:3 (2015).

http://www.mathnet.ru/eng/person8783
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/190414

Publications in Math-Net.Ru
2019
1. S. G. Tankeev, “On the standard conjecture for a fibre product of three elliptic surfaces with pairwise-disjoint discriminant loci”, Izv. RAN. Ser. Mat., 83:3 (2019),  213–256  mathnet  elib; Izv. Math., 83:3 (2019), 613–653  isi
2. S. G. Tankeev, “On the Standard Conjecture for a 3-Dimensional Variety Fibered over a Surface”, Mat. Zametki, 105:4 (2019),  643–644  mathnet  elib
2017
3. S. G. Tankeev, “On an inductive approach to the standard conjecture for a fibred complex variety with strong semistable degeneracies”, Izv. RAN. Ser. Mat., 81:6 (2017),  199–231  mathnet  elib; Izv. Math., 81:6 (2017), 1253–1285  isi  scopus
2015
4. S. G. Tankeev, “On the Brauer group of an arithmetic model of a hyperkähler variety over a number field”, Izv. RAN. Ser. Mat., 79:3 (2015),  203–224  mathnet  mathscinet  zmath  elib; Izv. Math., 79:3 (2015), 623–644  isi  scopus
5. S. G. Tankeev, “On the standard conjecture and the existence of a Chow–Lefschetz decomposition for complex projective varieties”, Izv. RAN. Ser. Mat., 79:1 (2015),  185–216  mathnet  mathscinet  zmath  elib; Izv. Math., 79:1 (2015), 177–207  isi  scopus
2014
6. S. G. Tankeev, “On the standard conjecture for complex 4-dimensional elliptic varieties and compactifications of Néron minimal models”, Izv. RAN. Ser. Mat., 78:1 (2014),  181–214  mathnet  mathscinet  zmath  elib; Izv. Math., 78:1 (2014), 169–200  isi  elib  scopus
7. S. G. Tankeev, “On the Finiteness of the Brauer Group of an Arithmetic Scheme”, Mat. Zametki, 95:1 (2014),  136–149  mathnet  mathscinet  elib; Math. Notes, 95:1 (2014), 122–133  isi  elib  scopus
2012
8. S. G. Tankeev, “On the standard conjecture for complex 4-dimensional elliptic varieties”, Izv. RAN. Ser. Mat., 76:5 (2012),  119–142  mathnet  mathscinet  zmath  elib; Izv. Math., 76:5 (2012), 967–990  isi  elib  scopus
2011
9. S. G. Tankeev, “On the standard conjecture of Lefschetz type for complex projective threefolds. II”, Izv. RAN. Ser. Mat., 75:5 (2011),  177–194  mathnet  mathscinet  zmath  elib; Izv. Math., 75:5 (2011), 1047–1062  isi  elib  scopus
2010
10. S. G. Tankeev, “On the standard conjecture of Lefschetz type for complex projective threefolds”, Izv. RAN. Ser. Mat., 74:1 (2010),  175–196  mathnet  mathscinet  zmath  elib; Izv. Math., 74:1 (2010), 167–187  isi  elib  scopus
2008
11. S. G. Tankeev, “On algebraic cycles on complex Abelian schemes over smooth projective curves”, Izv. RAN. Ser. Mat., 72:4 (2008),  197–224  mathnet  mathscinet  zmath  elib; Izv. Math., 72:4 (2008), 817–844  isi  elib  scopus
2007
12. S. G. Tankeev, “Monoidal transformations and conjectures on algebraic cycles”, Izv. RAN. Ser. Mat., 71:3 (2007),  197–224  mathnet  mathscinet  zmath  elib; Izv. Math., 71:3 (2007), 629–655  isi  elib  scopus
2005
13. S. G. Tankeev, “On the numerical equivalence of algebraic cycles on potentially simple Abelian schemes of prime relative dimension”, Izv. RAN. Ser. Mat., 69:1 (2005),  145–164  mathnet  mathscinet  zmath  elib; Izv. Math., 69:1 (2005), 143–162  isi  elib  scopus
2003
14. S. G. Tankeev, “On the Brauer group of an arithmetic scheme. II”, Izv. RAN. Ser. Mat., 67:5 (2003),  155–176  mathnet  mathscinet  zmath  elib; Izv. Math., 67:5 (2003), 1007–1029  isi  scopus
15. S. G. Tankeev, “On the standard conjecture for complex Abelian schemes over smooth projective curves”, Izv. RAN. Ser. Mat., 67:3 (2003),  183–224  mathnet  mathscinet  zmath; Izv. Math., 67:3 (2003), 597–635  isi  scopus
16. S. G. Tankeev, “On the Conjectures of Artin and Shafarevich–Tate”, Tr. Mat. Inst. Steklova, 241 (2003),  254–264  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 241 (2003), 238–248
2002
17. S. G. Tankeev, “The arithmetic and geometry of a generic hypersurface section”, Izv. RAN. Ser. Mat., 66:2 (2002),  173–204  mathnet  mathscinet  zmath; Izv. Math., 66:2 (2002), 393–424  scopus
2001
18. S. G. Tankeev, “On the Brauer group of an arithmetic scheme”, Izv. RAN. Ser. Mat., 65:2 (2001),  155–186  mathnet  mathscinet  zmath  elib; Izv. Math., 65:2 (2001), 357–388  scopus
19. S. G. Tankeev, “Cycles of small codimension on a simple abelian variety”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 70 (2001),  206–235  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 106:5 (2001), 3365–3382
20. S. G. Tankeev, “On the Mumford–Tate conjecture for abelian varieties”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 33 (2001),  213–241  mathnet  mathscinet  zmath; J. Math. Sci., 81:3 (1996), 2719–2737
2000
21. S. G. Tankeev, “On the Brauer group”, Izv. RAN. Ser. Mat., 64:4 (2000),  141–162  mathnet  mathscinet  zmath  elib; Izv. Math., 64:4 (2000), 787–806  isi  scopus
1999
22. S. G. Tankeev, “Cycles of small codimension on a simple $2p$- or $4p$-dimensional Abelian variety”, Izv. RAN. Ser. Mat., 63:6 (1999),  167–208  mathnet  mathscinet  zmath  elib; Izv. Math., 63:6 (1999), 1221–1262  isi  scopus
23. S. G. Tankeev, “On weights of the $l$-adic representation and arithmetic of Frobenius eigenvalues”, Izv. RAN. Ser. Mat., 63:1 (1999),  185–224  mathnet  mathscinet  zmath  elib; Izv. Math., 63:1 (1999), 181–218  isi  scopus
1998
24. S. G. Tankeev, “On Frobenius traces”, Izv. RAN. Ser. Mat., 62:1 (1998),  165–200  mathnet  mathscinet  zmath  elib; Izv. Math., 62:1 (1998), 157–190  isi  scopus
1996
25. S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”, Izv. RAN. Ser. Mat., 60:2 (1996),  159–194  mathnet  mathscinet  zmath; Izv. Math., 60:2 (1996), 391–424  isi  scopus
1995
26. S. G. Tankeev, “Surfaces of type K3 over number fields and the Mumford–Tate conjecture. II”, Izv. RAN. Ser. Mat., 59:3 (1995),  179–206  mathnet  mathscinet  zmath; Izv. Math., 59:3 (1995), 619–646  isi
1994
27. S. G. Tankeev, “Algebraic cycles on an abelian variety without complex multiplication”, Izv. RAN. Ser. Mat., 58:3 (1994),  103–126  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 44:3 (1995), 531–553  isi
28. S. G. Tankeev, “Cycles on an Abelian variety without complex multiplication and $l$-adic representations”, Uspekhi Mat. Nauk, 49:1(295) (1994),  225–226  mathnet  mathscinet  zmath; Russian Math. Surveys, 49:1 (1994), 247  isi
1993
29. S. G. Tankeev, “Abelian varieties and the general Hodge conjecture”, Izv. RAN. Ser. Mat., 57:4 (1993),  192–206  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 43:1 (1994), 179–191  isi
1991
30. S. G. Tankeev, “Kuga–Satake abelian varieties and $l$-adic representations”, Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991),  877–889  mathnet  mathscinet  zmath; Math. USSR-Izv., 39:1 (1992), 855–867  isi
1990
31. S. G. Tankeev, “K3 surfaces over number fields and the Mumford–Tate conjecture”, Izv. Akad. Nauk SSSR Ser. Mat., 54:4 (1990),  846–861  mathnet  mathscinet  zmath; Math. USSR-Izv., 37:1 (1991), 191–208
1988
32. S. G. Tankeev, “K3 surfaces over number fields and $l$-adic representations”, Izv. Akad. Nauk SSSR Ser. Mat., 52:6 (1988),  1252–1271  mathnet  mathscinet  zmath; Math. USSR-Izv., 33:3 (1989), 575–595
1987
33. S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987),  1214–1227  mathnet  mathscinet  zmath; Math. USSR-Izv., 31:3 (1988), 527–540
1983
34. S. G. Tankeev, “On cycles on Abelian varieties of prime dimension over finite or number fields”, Izv. Akad. Nauk SSSR Ser. Mat., 47:2 (1983),  356–365  mathnet  mathscinet  zmath; Math. USSR-Izv., 22:2 (1984), 329–337
1982
35. S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982),  155–170  mathnet  mathscinet  zmath; Math. USSR-Izv., 20:1 (1983), 157–171
1981
36. S. G. Tankeev, “On algebraic cycles on simple 5-dimensional Abelian varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 45:4 (1981),  793–823  mathnet  mathscinet  zmath; Math. USSR-Izv., 19:1 (1982), 95–123
37. S. G. Tankeev, “On algebraic cycles on surfaces and Abelian varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 45:2 (1981),  398–434  mathnet  mathscinet  zmath; Math. USSR-Izv., 18:2 (1982), 349–380
1979
38. S. G. Tankeev, “On algebraic cycles on Abelian varieties. II”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979),  418–429  mathnet  mathscinet  zmath; Math. USSR-Izv., 14:2 (1980), 383–394  isi
1978
39. S. G. Tankeev, “On algebraic cycles on Abelian varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 42:3 (1978),  667–696  mathnet  mathscinet  zmath; Math. USSR-Izv., 12:3 (1978), 617–643
1977
40. S. G. Tankeev, “On homomorphisms of Abelian schemes. II”, Izv. Akad. Nauk SSSR Ser. Mat., 41:6 (1977),  1231–1251  mathnet  mathscinet  zmath; Math. USSR-Izv., 11:6 (1977), 1175–1194
1976
41. S. G. Tankeev, “On homomorphisms of Abelian schemes”, Izv. Akad. Nauk SSSR Ser. Mat., 40:4 (1976),  774–790  mathnet  mathscinet  zmath; Math. USSR-Izv., 10:4 (1976), 731–747
1975
42. S. G. Tankeev, “Pluricanonical mappings of algebraic surfaces of general type”, Uspekhi Mat. Nauk, 30:6(186) (1975),  184  mathnet  mathscinet  zmath
1972
43. S. G. Tankeev, “On a global theory of moduli of algebraic surfaces of general type”, Izv. Akad. Nauk SSSR Ser. Mat., 36:6 (1972),  1220–1236  mathnet  mathscinet  zmath; Math. USSR-Izv., 6:6 (1972), 1200–1216
1971
44. S. G. Tankeev, “On $n$-dimensional canonically polarized varieties and varieties of fundamental type”, Izv. Akad. Nauk SSSR Ser. Mat., 35:1 (1971),  31–44  mathnet  mathscinet  zmath; Math. USSR-Izv., 5:1 (1971), 29–43
45. S. G. Tankeev, “Моноидальные преобразования и алгебраические соответствия”, Izv. RAN. Ser. Mat.,  0  mathnet

Presentations in Math-Net.Ru
1. Редукция гипотез Ходжа и Тэйта к случаю рациональных многообразий
S. G. Tankeev
Seminar of the Department of Algebra
October 5, 2004

Organisations
 
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