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

Wieslawa Niziol (1)

1 ENS Lyon - École normale supérieure - Lyon

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.

Domains: Mathematics [math]; Number Theory [math.NT]; Mathematics [math]; Algebraic Geometry [math.AG]

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