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BREUIL–KISIN–FARGUES MODULES WITH COMPLEX MULTIPLICATION

Published online by Cambridge University Press:  21 January 2020

Johannes Anschütz*
Affiliation:
Rheinische Friedrich-Wilhelms Universität Bonn, Mathematisches Institut, Bonn, Germany (ja@math.uni-bonn.de)

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’.

Type
Research Article
Copyright
© Cambridge University Press 2020

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BREUIL–KISIN–FARGUES MODULES WITH COMPLEX MULTIPLICATION
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