Families of Berkovich spaces /

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Bibliographic Details
Author / Creator:Ducros, Antoine, author.
Imprint:Paris : Société mathématique de France, 2018.
Description:vii, 262 pages : illustrations ; 24 cm.
Series:Astérisque, 0303-1179 ; 400
Astérisque ; 400.
Subject:Analytic spaces.
Zariski surfaces.
Arithmetical algebraic geometry.
Analytic spaces.
Arithmetical algebraic geometry.
Zariski surfaces.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11709456
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Notes:Includes bibliographical references (pages 259-262) and indexes.
In English. Abstract in English and French.
Summary:"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.