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GEOMETRIC SYNTOMIC COHOMOLOGY AND VECTOR BUNDLES ON THE FARGUES-FONTAINE CURVE

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 Crank. This dichotomy is reminiscent of the Hodge-Tate period map for p-divisible groups.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01420353
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Submitted on : Tuesday, December 20, 2016 - 2:43:29 PM
Last modification on : Thursday, November 28, 2019 - 11:50:55 PM
Long-term archiving on: : Monday, March 20, 2017 - 8:18:47 PM

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Wieslawa Niziol. GEOMETRIC SYNTOMIC COHOMOLOGY AND VECTOR BUNDLES ON THE FARGUES-FONTAINE CURVE. Journal of Algebraic Geometry, American Mathematical Society, 2019, 28, pp.605-648. ⟨ensl-01420353⟩

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