Les espaces de Berkovich sont excellents
| dc.creator | Ducros, Antoine | |
| dc.date | 2007-06-05 | |
| dc.date | 2009-01-27 | |
| dc.date.accessioned | 2026-07-07T12:34:09Z | |
| dc.date.available | 2026-07-07T12:34:09Z | |
| dc.description | In this paper, we first study the local rings of a Berkovich analytic space from the point of view of commutative algebra. We show that those rings are excellent ; we introduce the notion of a an analytically separable extension of non-archimedean complete fields (it includes the case of the finite separable extensions, and also the case of any complete extension of a perfect complete non-archimedean field) and show that the usual commutative algebra properties (Rm, Sm, Gorenstein, Cohen-Macaulay, Complete Intersection) are stable under analytically separable ground field extensions; we also establish a GAGA principle with respect to those properties for any finitely generated scheme over an affinoid algebra. A second part of the paper deals with more global geometric notions : we define, show the existence and establish basic properties of the irreducible components of analytic space ; we define, show the existence and establish basic properties of its normalization ; and we study the behaviour of connectedness and irreducibility with respect to base change. | |
| dc.description | This is the (almost) definitive version of the paper, which is going to appear in "Annales de l'institut Fourier" | |
| dc.identifier | https://arxiv.org/abs/0706.0666 | |
| dc.identifier | http://arxiv.org/abs/0706.0666 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217323 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G22, 14B99 | |
| dc.title | Les espaces de Berkovich sont excellents | |
| dc.type | text |