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arXiv · 1605.07216

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

Wieslawa Niziol
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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 $Q_p$-vector spaces for ordinary varieties, but in the nonordinary case, these cohomology Spaces carry much more information, in particular they can have a non-trivial $C$-rank. This dichotomy is reminiscent of the Hodge-Tate period map for $p$-divisible groups.

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Wieslawa Niziol. 2016-05-23. Geometric syntomic cohomology and vector bundles on the Fargues-Fontaine curve. https://arxiv.org/abs/1605.07216

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