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- D Logachev
- 2004

Ideas and methods of Clemens C.H., Griffiths Ph. The intermediate Jacobian of a cubic threefold are applied to a Fano threefold X of genus 6 — intersection of G(2, 5) ⊂ P 9 with P 7 and a quadric. We prove: 1. The Fano surface F (X) of X is smooth and irreducible. Hodge numbers and some other invariants of F (X) are calculated. 2. Tangent bundle theorem for… (More)

- D. Logachev
- 2005

In his earlier paper the author offered a program of generalization of Kolyvagin’s result of finiteness of SH to the case of some motives which are quotients of cohomology motives of Shimura varieties. The present paper is devoted to the first step of this program — finding of an analog of Kolyvagin’s trace relations for Siegel sixfolds and for the Hecke… (More)

- D. Logachev
- 2009

An analogy between abelian Anderson T-motives of rank r and dimension n , and abelian varieties over C with multiplication by an imaginary quadratic field K, of dimension r and of signature (n, r − n), permits us to get two elementary results in the theory of abelian varieties. Firstly, we can associate to this abelian variety a (roughly speaking) K-vector… (More)

- D Yu Logachev
- 2007

1 1. Introduction. 1.1. The purpose of the present paper is to prove some important steps of a natural program of generalization of Kolyvagin's proof of niteness of Tate-Shafarevich group of a Taniyama-Weil elliptic curve E of analytic rank 0 or 1 ((K1], K2], referred below as \K-case") to the case of other Shimura varieties. Some intermediate results of… (More)

- Dmitry Logachev
- 2008

There exist conjectural formulas on relations between L-functions of submotives of Shimura varieties and automorphic representations of the corresponding reductive groups, due to Langlands — Arthur. In the present paper these formulas are used in order to get explicit relations between eigenvalues of p-Hecke operators (generators of the p-Hecke algebra of… (More)

We introduce the notion of duality for an abelian Anderson T-motive M . Main results of the paper (all M have N = 0): 1. Algebraic duality implies analytic duality (Theorem 4.4). Explicitly, this means that a Siegel matrix of the dual of a uniformizable M is the minus transposed of a Siegel matrix of M . 2. There is a 1 – 1 correspondence between pure… (More)

- Alexander N. Grishkov, D. Logachev
- Finite Fields and Their Applications
- 2016

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