**Title:** On the support problem for the intermediate jacobians of l-adic representations

**Speaker:** Professor Wojciech Gajda

**Speaker Info:** Poznan University

**Brief Description:**

**Special Note**:

**Abstract:**

In the talk I am going to discuss joint work with Grzegorz Banaszak and Piotr Krason on the support problem of Erdos in the context of l-adic representations of the absolute Galois group of a number field.Roughly speaking, the support problem for an abelian variety A, defined over a number field F, asks for a relation between two nontorsion points of the Mordell-Weil group A(F), if we know that the reductions of the two points are dependent over the residue field, for infinitely many primes of reduction. The main applications of our work concern abelian varieties with real and complex multiplications, as well as the algebraic K-theory groups of number fields, and the integral homology of the general linear groups of rings of integers.

We answer the question of Corrales-Rodriganez and Schoof concerning the support problem for higher dimensional abelian varieties. At a technical point in the proof we verify the Mumford-Tate conjecture on the image of the Tate module represenation, for those RM abelian varieties with which we work.

The preprint of the paper is already available in the Algebraic Number Theory and in the Algebraic K-theory archives.

Copyright © 1997-2024 Department of Mathematics, Northwestern University.