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- G. Banaszak, W. Gajda, P. Krasoń
- 2005

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)

4 The Euler system {Λ(L, r̄); L ∈ S} and K∗(Z) 15 4.1 Divisible elements in K2n(Q) for n odd. . . . . . . . . . . . . . . . . . . . . 15 4.2 Kolyvagin operator and elements δn(L) . . . . . . . . . . . . . . . . . . . . 15 4.3 Elements K(L, r̄) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.4 Etale cohomology and Chebotarev density… (More)

- Dominique Arlettaz, Grzegorz Banaszak

- G. Banaszak, P. Krasoń
- 2009

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)

- G. Banaszak, W. Gajda, P. Krasoń
- 2008

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)

- G. Banaszak
- 2008

In this paper we investigate the image of the l-adic representation attached to the Tate module of an abelian variety over a number field with endomorphism algebra of type I or II in the Albert classification. We compute the image explicitly and verify the classical conjectures of Mumford-Tate, Hodge, Lang and Tate, for a large family of abelian varieties… (More)

In this paper we establish a Hasse principle concerning the linear dependence over Z of nontorsion points in the Mordell-Weil group of an abelian variety over a number field.

- Grzegorz Banaszak, Piotr Zelewski
- 2007

In this paper we prove that K-groups of the henselization of some local rings imbed into K-groups of the completion of these rings. One of the main tools we use is the Artin Approximation Theorem.