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Espaces de Banach-Colmez et faisceaux coh\'erents sur la courbe de Fargues-Fontaine

Abstract : We give a new definition, simpler but equivalent, of the abelian category of Banach-Colmez spaces introduced by Colmez, and we explain the precise relationship with the category of coherent sheaves on the Fargues-Fontaine curve. One goes from one category to the other by changing the t-structure on the derived category. Along the way, we obtain a description of the pro-\'etale cohomology of the open disk and the affine space, of independent interest.
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https://hal.archives-ouvertes.fr/hal-03018431
Contributor : Arthur-César Le Bras Connect in order to contact the contributor
Submitted on : Friday, November 26, 2021 - 11:55:15 AM
Last modification on : Wednesday, December 1, 2021 - 1:34:09 PM

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Arthur-César Le Bras. Espaces de Banach-Colmez et faisceaux coh\'erents sur la courbe de Fargues-Fontaine. Duke Mathematical Journal, Duke University Press, 2018, ⟨10.1215/00127094-2018-0034⟩. ⟨hal-03018431⟩

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