Cohomologie analytique des arrangements d'hyperplans

DOI10.2140/ANT.2023.17.1arXiv2012.12729MaRDI QIDQ6356804

Publication date: 23 December 2020

Abstract: In this article, we study the cohomology of some analytic sheaves on the complementary in the projective space of a suitable infinite collection of hyperplane like the Drinfel'd symetric space. In particular, the sheaf of invertible functions on these rigid spaces has no cohomology in degree greater or equal to

1

. This proves the vanishing of the Picard goup and the methods used give a convenient description of the global invertible functions.

Mathematics Subject Classification ID

Analytic sheaves and cohomology groups (32C35) Non-Archimedean analysis (32P05)

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