Families of Berkovich spaces
By: Antoine Ducros
Series: Astérisque -- 400; Astérisque -- 400.
Publisher: Société mathématique de France
Published: 2018
Place of publication: Paris
Language: eng
Number of pages: 262
ISBN-13: 9782856298855
Copyright date: 2018
Subjects: Analytic spaces; Zariski surfaces; Arithmetical algebraic geometry
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.
Notes: Includes bibliographical references (pages 259-262) and indexes.

In English. Abstract in English and French.
Table of contents: title: Background material; title: Algebraic properties in analytic geometry; title: Germs, Temkin's reduction and [gamma]-strictness; title: Flatness in analytic geometry; title: Quasi-smooth morphisms; title: Generic fibers in analytic geometry; title: Images of morphisms : local results; title: Dévissages á la Raynaud-Gruson; title: Quasi-finite multisections and images of maps; title: Constructable loci; title: Algebraic properties : targes, fibers and source; title: Graded commutative algebra.