Cohomologie analytique des arrangements d'hyperplans
Number Theory
2023-02-22 v3 Algebraic Geometry
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 . This proves the vanishing of the Picard goup and the methods used give a convenient description of the global invertible functions.
Cite
@article{arxiv.2012.12729,
title = {Cohomologie analytique des arrangements d'hyperplans},
author = {Damien Junger},
journal= {arXiv preprint arXiv:2012.12729},
year = {2023}
}
Comments
38 pages, in french. To be appeared in "Algebra & Number Theory" journal