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Journal of the Institute of Mathematics of Jussieu (1)

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BREUIL–KISIN–FARGUES MODULES WITH COMPLEX MULTIPLICATION
Part of
- (Co)homology theory
- Arithmetic rings and other special rings
Johannes Anschütz
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 6 / November 2021

Published online by Cambridge University Press:

21 January 2020, pp. 1855-1904

Print publication:

November 2021
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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’.