On the structure theory of the Iwasawa algebra of a p-adic Lie group

Venjakob, Otmar. "On the structure theory of the Iwasawa algebra of a p-adic Lie group." Journal of the European Mathematical Society 004.3 (2002): 271-311. <http://eudml.org/doc/277361>.

@article{Venjakob2002,
abstract = {This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, $\Lambda $ of a $p$-adic analytic group $G$. For $G$ without any $p$-torsion element we prove that $\Lambda $ is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null $\Lambda $-module. This is classical when $G=\mathbb \{Z\}^k_p$ for some integer $k\ge 1$, but was previously unknown in the non-commutative case. Then the category of $\Lambda $-modules up to pseudo-isomorphisms is studied and we obtain a weak structure theorem for the $\mathbb \{Z\}_p$-torsion part of a finitely generated $\Lambda $-module. We also prove a local duality theorem and a version of Auslander-Buchsbaum equality. The arithmetic applications to the Iwasawa theory of abelian varieties are published elsewhere.},
author = {Venjakob, Otmar},
journal = {Journal of the European Mathematical Society},
keywords = {finitely generated modules; Iwasawa algebras; completed group algebras; $p$-adic analytic groups; Auslander regular rings; categories of modules; finitely generated modules; Iwasawa algebras; completed group algebras; -adic analytic groups; Auslander regular rings; categories of modules},
language = {eng},
number = {3},
pages = {271-311},
publisher = {European Mathematical Society Publishing House},
title = {On the structure theory of the Iwasawa algebra of a p-adic Lie group},
url = {http://eudml.org/doc/277361},
volume = {004},
year = {2002},
}

TY - JOUR
AU - Venjakob, Otmar
TI - On the structure theory of the Iwasawa algebra of a p-adic Lie group
JO - Journal of the European Mathematical Society
PY - 2002
PB - European Mathematical Society Publishing House
VL - 004
IS - 3
SP - 271
EP - 311
AB - This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, $\Lambda $ of a $p$-adic analytic group $G$. For $G$ without any $p$-torsion element we prove that $\Lambda $ is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null $\Lambda $-module. This is classical when $G=\mathbb {Z}^k_p$ for some integer $k\ge 1$, but was previously unknown in the non-commutative case. Then the category of $\Lambda $-modules up to pseudo-isomorphisms is studied and we obtain a weak structure theorem for the $\mathbb {Z}_p$-torsion part of a finitely generated $\Lambda $-module. We also prove a local duality theorem and a version of Auslander-Buchsbaum equality. The arithmetic applications to the Iwasawa theory of abelian varieties are published elsewhere.
LA - eng
KW - finitely generated modules; Iwasawa algebras; completed group algebras; $p$-adic analytic groups; Auslander regular rings; categories of modules; finitely generated modules; Iwasawa algebras; completed group algebras; -adic analytic groups; Auslander regular rings; categories of modules
UR - http://eudml.org/doc/277361
ER -