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.
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).
