Wojciech Gajda

Publications (8)0 Total impact

• Source

  Available from: arxiv.org

  Article: On the image of l-adic Galois representations for abelian varieties of type I and II

  Grzegorz Banaszak, Wojciech Gajda, Piotr Krason
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  ABSTRACT: 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 of type I and II. In addition, for this family, we prove an analogue of the open image theorem of Serre.
  08/2004;
• Source

  Available from: arxiv.org

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

  Grzegorz Banaszak, Wojciech Gajda, Piotr Krason
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  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.
  01/2003;
• Article: On 2-adic cyclotomic elements in K-theory and étale cohomology of the ring of integers

  Dominique Arlettaz, Grzegorz Banaszak, Wojciech Gajda
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  ABSTRACT: In this paper we define 2-adic cyclotomic elements in K-theory and Étale cohomology of the integers. We construct a comparison map which sends the 2-adic elements in K-theory onto 2-adic elements in cohomology. We also compute explicitly some of the product maps in K-theory of Z at the prime 2:
  05/1999;
• Source

  Available from: psu.edu

  Article: Euler Systems for Higher K-theory of number fields

  Grzegorz Banaszak, Wojciech Gajda
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  ABSTRACT: this paper we investigate elements in higher K-groups of a number field which behave similarly to the Euler system of Gauss sums used by K.Rubin in [Ru2] in his proof of "the Main Conjecture" in Iwasawa theory.
  01/1999;
• Article: On the Arithmetic of Cyclotomic Fields and the K-theory of Q

  Grzegorz Banaszak, Wojciech Gajda
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  ABSTRACT: . In the present work, we investigate divisible elements in the group K2n (Q) in connection with conjectures of Kummer-Vandiver and Iwasawa. The main result of the paper gives a description of divisible elements in terms of special elements in K-theory. We also define a divisibility height function and prove its basic properties. 1. Introduction One of the mysteries of algebraic K-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( l ) and E = Q( l k ). We fix a primitive root of unity l k of order l k : Let A and A [i] denote the l-Sylow subgroup of the ideal class group of F and the ith eigenspace of A under the action of the Galois group G(F=Q), respectively. Let A + be the direct sum of A [i] with i even cf. [12, p.100]. There are two famous conjectures in number theory which concern the class group of the cyclotomic field F . Conjectu...
  01/1999;
• Article: Algebraic K-theory / Grzegorz Banaszak, Wajciech Gajda, Piotr Krason editors

  Grzegorz Banaszak, Wojciech Gajda, Piotr Krason
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  ABSTRACT: Paper from a conference held Sept. 1995 in Poznan, Poland Incluye bibliografía
  SERBIULA (sistema Librum 2.0).
• Source

  Available from: gwdg.de

  Article: On the image of Galois $l$-adic representations for abelian varieties of type III

  Grzegorz Banaszak, Wojciech Gajda, Piotr Krasoń
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  ABSTRACT: 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.
• Source

  Available from: psu.edu

  Article: On Galois representations for abelian varieties with complex and real multiplications

  Wojciech Gajda, Grzegorz Banaszak, Piotr Krasoń
  Journal of Number Theory, v.100, 117-132 (2003).