Wojciech Gajda

Support problem for the intermediate Jacobians of l-adic representations

Abstract We consider the support problem of Erdos in the context of l-adic representations of the absolute Galois group of a number field. Main applications of the results of the paper concern Galois cohomology of the Tate module of abelian varieties with real and complex multiplications, the algebraic K-theory groups of number fields and the integral homology of the general linear group of rings of integers. We answer the question of Corrales-Rodriganez and Schoof concerning the support problem for higher dimensional abelian varieties.

Linear dependence in Mordell-Weil groups

Abstract Let A be an abelian variety defined over a number field F. Let P be a point in the Mordell-Weil group A(F) and H a subgroup of A(F). We consider the following local-global principle originated with the support problem of Erdös for the integers: the point P belongs to the group H, if for almost all primes v of F, the point P (modulo v) belongs to the group H (modulo v). We prove that the principle holds for any abelian variety A, if H is a free submodule and the point P generates a free submodule of A(F) over the ring End F A.

On Galois representations for abelian varieties with complex and real multiplications

Abstract In this paper, we study the image of l-adic representations coming from Tate module of an abelian variety defined over a number field. We treat abelian varieties with complex and real multiplications. We verify the Mumford–Tate conjecture for a new class of abelian varieties with real multiplication.

A support problem for K -theory of number fields☆

In this paper we consider a support problem for the reduction map in the odd K -theory of number fields.

Independence of -adic Galois representations over function fields

Let

A Note on the Quillen–Lichtenbaum Conjecture and the Arithmetic of Square Rings

K

On the map between homology of henselization and completion of some local rings

be a finitely generated extension of

Detecting linear dependence by reduction maps

\mathbb{Q}

On the Image of l-Adic Galois Representations for Abelian Varieties of Type I and II

. We consider the family of

Euler Systems for HigherK-Theory of Number Fields

\ell