Grzegorz Banaszak

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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(More)
In this paper we investigate linear dependence of points in Mordell-Weil groups of abelian varieties via reduction maps. In particular we try to determine the conditions for detecting linear dependence in Mordell-Weil groups via finite number of reductions.
One of the mysteries of algebraicK-theory is its relation to classical conjectures of number theory. Before we recall some instances of the relation let us introduce the necessary notation. For an odd prime l, let F = Q(μl) and E = Q(μlk ). We fix a primitive root of unity ξlk of order l . Let A and A denote the l-Sylow subgroup of the ideal class group of(More)
We consider the support problem of Erdös 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(More)