7 research outputs found
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 -adic representations for abelian varieties of type III
In this paper we investigate the image of the -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 -adic and mod 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