On the structure theory of the Iwasawa algebra of a p-adic Lie group |
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Authors: | Otmar Venjakob |
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Institution: | Universit?t Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, 69120 Heidelberg, Germany, e-mail: otmar@mathi.uni-heidelberg.de, http://www.mathi.uni-heidelberg.de/~otmar/, DE
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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, Λ of a p-adic analytic group G. For G without any p-torsion element we prove that Λ is an Auslander regular ring. This result enables us to give a good definition of the notion
of a pseudo-nullΛ-module. This is classical when G=ℤ
k
p
for some integer k≥1, but was previously unknown in the non-commutative case. Then the category of Λ-modules up to pseudo-isomorphisms is studied
and we obtain a weak structure theorem for the ℤ
p
-torsion part of a finitely generated Λ-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.
Received May 12, 2001 / final version received July 5, 2001?Published online September 3, 2001 |
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Keywords: | Mathematics Subject Classification (2000): 16D70 16E30 16E65 16S34 |
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