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Journal Articles Journal of Algebraic Geometry Year : 2019

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

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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 Crank. This dichotomy is reminiscent of the Hodge-Tate period map for p-divisible groups.
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ensl-01420353 , version 1 (20-12-2016)

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  • HAL Id : ensl-01420353 , version 1

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

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