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

Journal of the European Mathematical Society (2002)

- Volume: 004, Issue: 3, page 271-311
- ISSN: 1435-9855

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topVenjakob, 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 -

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