A support problem for the intermediate Jacobians of l-adic representations

TL;DR

This paper investigates the support problem related to the intermediate Jacobians of l-adic representations, focusing on Galois representations and the Mumford-Tate conjecture for certain abelian varieties with complex and real multiplication.

Contribution

The paper provides new insights into the support problem for intermediate Jacobians and explores Galois representations for abelian varieties with complex and real multiplication.

Findings

Results on the image of Galois representations

Progress on the Mumford-Tate conjecture for RM abelian varieties

Subdivision of the original work into two focused parts

Abstract

This is a revised version of ANT-0332: "A support problem for the intermediate Jacobians of l-adic representations", by G. Banaszak, W. Gajda & P. Krason, which was placed on these archives on the 29th of January 2002. Following a suggestion of the referee we have subdivided the paper into two separate parts: "Support problem for the intermediate Jacobians of l-adic representations", and "On Galois representations for abelian varieties with complex and real multiplications". Our results on the image of Galois and the Mumford-Tate conjecture for some RM abelian varieties are contained in the second paper. Both papers were accepted for publication.