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Un résultat de connexité pour les variétés analytiques p-adiques. Privilège et noethérianité
Un résultat de connexité pour les variétés analytiques p-adiques. Privilège et noethérianité
- Source :
- Compositio Mathematica, Compositio Mathematica, 2008, 144 (1), pp.107-133, Compositio Mathematica, Foundation Compositio Mathematica, 2008, 144 (1), pp.107-133
- Publication Year :
- 2008
- Publisher :
- HAL CCSD, 2008.
-
Abstract
- Let $k$ be a non-Archimedean field, $X$ a $k$-affinoid space and $f$ an analytic function over $X$. We precisely describe how the geometric connected components of the spaces $\{x \in X, |f(x)| \ge \varepsilon\}$ behave with regards to $\varepsilon$. We also obtain a result concerning privileged neighbourhoods and adapt a theorem from complex analytic geometry about Noetherianity for germs of analytic functions.<br />Comment: Slight improvements of theorems 1 and 2. Final version. 46 pages
- Subjects :
- Pure mathematics
espaces de Berkovich
Field (mathematics)
Space (mathematics)
01 natural sciences
Domain (mathematical analysis)
noethérianité
Mathematics - Algebraic Geometry
Analytic geometry
0103 physical sciences
0101 mathematics
Mathematics
Connected component
14G22
Algebra and Number Theory
010102 general mathematics
MSC 14G22
schémas formels
16. Peace & justice
[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]
géométrie analytique rigide
ComputingMethodologies_DOCUMENTANDTEXTPROCESSING
010307 mathematical physics
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
privilège
Analytic function
Subjects
Details
- Language :
- French
- ISSN :
- 0010437X and 15705846
- Database :
- OpenAIRE
- Journal :
- Compositio Mathematica, Compositio Mathematica, 2008, 144 (1), pp.107-133, Compositio Mathematica, Foundation Compositio Mathematica, 2008, 144 (1), pp.107-133
- Accession number :
- edsair.doi.dedup.....1f82dca57e20fcac5e0447804804a683