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On the Iwasawa theory of the Lubin–Tate moduli space

Part of: Algebraic number theory: local and $p$-adic fields Locally compact groups and their algebras Algebraic groups

Published online by Cambridge University Press:  26 February 2013

Jan Kohlhaase
Jan Kohlhaase*
Affiliation:
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, D-48149 Münster, Germany (email: kohlhaaj@math.uni-muenster.de)
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Abstract

We study the affine formal algebra $R$ of the Lubin–Tate deformation space as a module over two different rings. One is the completed group ring of the automorphism group $\Gamma $ of the formal module of the deformation problem, the other one is the spherical Hecke algebra of a general linear group. In the most basic case of height two and ground field $\mathbb {Q}_p$, our structure results include a flatness assertion for $R$ over the spherical Hecke algebra and allow us to compute the continuous (co)homology of $\Gamma $ with coefficients in $R$.

Keywords

moduli spacesformal groups$p$-adic representation theory

MSC classification

Secondary: 14L05: Formal groups, $p$-divisible groups 22D10: Unitary representations of locally compact groups 11S23: Integral representations

Information

Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 5 , May 2013 , pp. 793 - 839
Copyright
Copyright © 2013 The Author(s) 

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