Cohomologie analytique des arrangements d'hyperplans

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.

38 pages, in french. To be appeared in "Algebra & Number Theory" journal

References in corpus (1)

• Invertible functions on non-archimedean symmetric spaces

Cited by in corpus (1)

• On the $v$-Picard group of Stein spaces