Espaces de Banach-Colmez et faisceaux coh\’erents sur la courbe de Fargues-Fontaine Article - 2018

Arthur-César Le Bras

Arthur-César Le Bras, « Espaces de Banach-Colmez et faisceaux coh\’erents sur la courbe de Fargues-Fontaine  », Duke Mathematical Journal, 2018. ISSN 0012-7094

Résumé

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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