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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Geometric syntomic cohomology and vector bundles on the Fargues-Fontaine curve

Author: Wiesława Nizioł
Journal: J. Algebraic Geom. 28 (2019), 605-648
Published electronically: June 28, 2019
MathSciNet review: 3994308
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Abstract | References | Additional Information

Abstract: We show that geometric syntomic cohomology lifts canonically to the category of Banach-Colmez spaces and study its relation to extensions of modifications of vector bundles on the Fargues-Fontaine curve. We include some computations of geometric syntomic cohomology spaces: they are finite rank $\mathbf {Q}_p$-vector spaces for ordinary varieties, but in the nonordinary case, these cohomology spaces carry much more information; in particular they can have a nontrivial $C$-rank. This dichotomy is reminiscent of the Hodge-Tate period map for $p$-divisible groups.

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Additional Information

Wiesława Nizioł
Affiliation: UMPA, École Normale Supérieure de Lyon, 46, allée d’Italie, 69007 Lyon, France

Received by editor(s): June 9, 2016
Received by editor(s) in revised form: February 12, 2019, and April 9, 2019
Published electronically: June 28, 2019
Additional Notes: The author’s research was supported in part by the grant ANR-14-CE25.
Article copyright: © Copyright 2019 University Press, Inc.