Families of Berkovich spaces

Astérisque. n° 400

de

chez Société mathématique de France

Paru le | Broché 262 pages

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Présentation en anglais


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.
Une étude sur les espaces de Berkovich et les notions mathématiques qu'ils impliquent. ©Electre 2019
Format : Broché
Nb de pages : 262 pages
Poids : 400 g
Dimensions : 18cm X 24cm
Date de parution :
ISBN : 978-2-85629-885-5
EAN : 9782856298855