$K_0$-invariance of the completely faithful property of Iwasawa modules

Autor:	Csige, Tamas
Rok vydání:	2014
Předmět:	Mathematics - Representation Theory Mathematics - Number Theory 11R23 19A31 22E35
Druh dokumentu:	Working Paper
Popis:	Let $H$ be a compact $p$-adic analytic group without torsion element, whose Lie algebra is split semisimple and $\mathfrak{N}_H(G)$ be the full subcategory of the category of finitely generated modules over the Iwasawa algebra $\Lambda_G$ that are also finitely generated as $\Lambda_H$-modules, where $G = \mathbb{Z}_{p} \times H$. We show that if the class of a module $N$ in the Grothendieck group of $\mathfrak{N}_H(G)$ equals to the class of a completely faithful module, then $q(N)$ is also completely faithful, where $q(N)$ denotes the image of $N$ via the quotient functor modulo the full subcategory of pseudonull modules. We also generalize a Theorem of Konstantin Ardakov characterizing the completely faithful property to the case of more general $p$-adic Lie groups. Comment: 10 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1408.3483 Zobrazit plný text záznamu View this record from Arxiv