Piotr Krasoń

Support problem for the intermediate Jacobians of l-adic representations

Abstract We consider the support problem of Erdos 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 the general linear group of rings of integers. We answer the question of Corrales-Rodriganez and Schoof concerning the support problem for higher dimensional abelian varieties.

On Galois representations for abelian varieties with complex and real multiplications

Abstract In this paper, we study the image of l-adic representations coming from Tate module of an abelian variety defined over a number field. We treat abelian varieties with complex and real multiplications. We verify the Mumford–Tate conjecture for a new class of abelian varieties with real multiplication.

A support problem for K -theory of number fields☆

In this paper we consider a support problem for the reduction map in the odd K -theory of number fields.

A direct variational method for the determination of the equivalent time constant of diffusion processes

Abstract The Ritz variational method is suggested for use in the determination of the equivalent time constant of diffusion processes. General formulas are obtained and illustrated with examples.

A Note on the Quillen–Lichtenbaum Conjecture and the Arithmetic of Square Rings

v W(Fv) → W (F ) → 0, where v runs over finite places of F. In [B] the group K 2n(O)l was called the l-part of the wild kernel for K2n(F ). We expect that the groups WK2n(F )l and K w 2n(O)l coincide. It is unknown in the moment, since we do not know the K-theory with coefficients in Z/l of a local field in the case when l is divisible by the residue characteristic, except for the case of Ql which follows by results of Bökstedt and Madsen [BM].

On the map between homology of henselization and completion of some local rings

Abstract In this note we prove that the integral homology of the special linear group of the henselization of some local rings imbeds into the homology of the special linear group of the completion. We define henselian adele ring and prove that the integral homology of its special linear group injects into the homology of Sl of the finite adele ring. The method of the proof is based on an application of the Artin approximation theorem to the bar complex which calculates the homology.