Families of Berkovich spaces
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Author
Publication
2018 - Société mathématique de France, Paris, France
Language
English
Word Count
65,500 words, Guess
Page Count
262 pages
Identifiers
- ISBN-102856298850
- ISBN-139782856298855
- OCLC Control Number1048929119
- Open LibraryOL44198154M
Classifications
- LCCQA331 .D83 2018
- LCCQA1 .A85 no. 400
Description
"This book investigates, roughly speaking, the variation of the properties of the fibers of a map between analytic spaces in the sense of Berkovich. First of all, we study flatness in this setting; the naive definition of this notion is not reasonable, we explain why and give another one. We then describe the loci of fiberwise validity of some usual properties (like being Cohen-Macaulay, Gorenstein, geometrically regular...); we show that these are (locally) Zariski-constructible subsets of the source space. For that purpose, we develop systematic methods for 'spreading out' in Berkovich geometry, as one does in scheme theory, some properties from a 'generic' fiber to a neighborhood of it"--Page 4 of cover.
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