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BREUIL–KISIN–FARGUES MODULES WITH COMPLEX MULTIPLICATION

Part of: Arithmetic rings and other special rings (Co)homology theory

Published online by Cambridge University Press:  21 January 2020

Johannes Anschütz Open the ORCID record for Johannes Anschütz [Opens in a new window]
Johannes Anschütz*
Affiliation:
Rheinische Friedrich-Wilhelms Universität Bonn, Mathematisches Institut, Bonn, Germany (ja@math.uni-bonn.de)
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Abstract

We prove that the category of (rigidified) Breuil–Kisin–Fargues modules up to isogeny is Tannakian. We then introduce and classify Breuil–Kisin–Fargues modules with complex multiplication mimicking the classical theory for rational Hodge structures. In particular, we compute an avatar of a ‘$p$-adic Serre group’.

Keywords

p-adic Hodge theorycomplex multiplicationTannakian categorieslocal Galois representations

MSC classification

Primary: 14F30: $p$-adic cohomology, crystalline cohomology 13F35: Witt vectors and related rings

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 6 , November 2021 , pp. 1855 - 1904
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Copyright
© Cambridge University Press 2020

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