Detecting linear dependence by reduction maps

We consider the local to global principle for detecting linear dependence of points in groups of the Mordell-Weil type. As applications of our general setting we obtain corresponding statements for Mordell-Weil groups of non{-}CM elliptic curves and some higher dimensional abelian varieties defined over number fields, and also for odd dimensional K-groups of number fields.Comment: This is a revised version of the MPI preprint no. 14 from March 200

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

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

On the image of Galois ll-adic representations for abelian varieties of type III

In this paper we investigate the image of the $l$-adic representation attached to the Tate module of an abelian variety defined over a number field. We consider simple abelian varieties of type III in the Albert classification. We compute the image of the $l$-adic and mod $l$ Galois representations and we prove the Mumford-Tate and Lang conjectures for a wide class of simple abelian varieties of type III

Stable K-theory and topological Hochschild homology of A [infty] rings

Schwänzl R, Staffeldt R, Waldhausen F. Stable K-theory and topological Hochschild homology of A [infty] rings. In: Banaszak G, Gajda W, Krason P, eds. Algebraic K-theory: Conference on Algebraic K-Theory, September 4 - 8, 1995, The Adam Mickiewicz University, Poznan, Poland. Contemporary mathematics ; 199. Providence, RI: American Mathematical Society; 1996: 161-173