On twists of modules over non-commutative Iwasawa algebras

It is well known that, for any finitely generated torsion module M over the Iwasawa algebra Z_p [[{\Gamma} ]], where {\Gamma} is isomorphic to Z_p, there exists a continuous p-adic character {\rho} of {\Gamma} such that, for every open subgroup U of {\Gamma}, the group of U-coinvariants M({\rho})_U is finite; here M( {\rho}) denotes the twist of M by {\rho}. This twisting lemma was already applied to study various arithmetic properties of Selmer groups and Galois cohomologies over a cyclotomic tower by Greenberg and Perrin-Riou. We prove a non commutative generalization of this twisting lemma replacing torsion modules over Z_p [[ {\Gamma} ]] by certain torsion modules over Z_p [[G]] with more general p-adic Lie group G.Comment: submitte

ENDOSCOPIC CONGRUENCES AND ADJOINT LL-VALUES FOR GSp(4) (Analytic, geometric and pp-adic aspects of automorphic forms and LL-functions)

In this article, we present the result of [1018] on the congruence between cuspidal automorphic representations of GSp₄ , which is a joint article with Francesco Lemma

On the Selmer groups of abelian varieties over function fields of characteristic p>0

In this paper, we study a (p-adic) geometric analogue for abelian varieties over a function field of characteristic p of the cyclotomic Iwasawa theory and the non-commutative Iwasawa theory for abelian varieties over a number field initiated by Mazur and Coates respectively. We will prove some analogue of the principal results obtained in the case over a number field and we study new phenomena which did not happen in the case of number field case. We propose also a conjecture which might be considered as a counterpart of the principal conjecture in the case over a number field. \par This is a preprint which is distributed since 2005 which is still in the process of submision. Following a recent modification of some technical mistakes in the previous version of the paper as well as an amelioration of the presentation of the paper, we decide wider distribution via the archive.Comment: 21 page