Tamas Csige | Searcharxiv

arXiv2016

The Grothendieck group of completed distribution algebras

Let $G$ be a compact $p$-adic analytic group with no element of order $p$ and $H$ be its maximal uniform normal subgroup. Let $K$ be a finite extention of $\mathbb{Q}_p$. We show that the Grothendieck group of the completion of the algebra of locally analytic distributions on $G$ is isomorphic to $\mathbb{Z}^c$ where $c$ is the number of conjugacy classes in $G/H$ relative prime to $p$, provided that $K$ is big enough. In addition we will see the algebra $K[[G]]$ of continuous distributions on $G$ has the same Grothendieck group.

math.KT↗

arXiv2015

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

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 $Λ_G$ that are also finitely generated as $Λ_H$-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.

math.RT↗