Mathematics – Algebraic Geometry
Scientific paper
2007-06-05
Mathematics
Algebraic Geometry
This is the (almost) definitive version of the paper, which is going to appear in "Annales de l'institut Fourier"
Scientific paper
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.
No associations
LandOfFree
Les espaces de Berkovich sont excellents does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Les espaces de Berkovich sont excellents, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Les espaces de Berkovich sont excellents will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-122519