Generalized Robba rings

We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact p -adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In the Appendix a “generalized Robba ring” for uniform pro- p gr...

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Bibliographic Details
Published in:Israel journal of mathematics 2012-10, Vol.191 (2), p.817-887
Main Author: Zábrádi, Gergely
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact p -adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In the Appendix a “generalized Robba ring” for uniform pro- p groups is constructed which naturally contains the locally analytic distribution algebra as a subring. The construction uses the theory of generalized microlocalization of quasi-abelian normed algebras that is also developed there. We equip this generalized Robba ring with a selfdual locally convex topology extending the topology on the distribution algebra. This is used to show some results on coadmissible modules.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-012-0013-4