Families of Berkovich spaces / Antoine Ducros.

Format:

Book

Author/Creator:

Ducros, Antoine, author.

Series:

Astérisque ; 400.

Astérisque, 0303-1179 ; 400

Language:

English

French

Subjects (All):

Analytic spaces.

Zariski surfaces.

Arithmetical algebraic geometry.

Physical Description:

vii, 262 pages : illustrations ; 24 cm.

Place of Publication:

Paris : Société mathématique de France, 2018.

Language Note:

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.

Contents:

Background material

Algebraic properties in analytic geometry

Germs, Temkin's reduction and [gamma]-strictness

Flatness in analytic geometry

Quasi-smooth morphisms

Generic fibers in analytic geometry

Images of morphisms : local results

Dévissages á la Raynaud-Gruson

Quasi-finite multisections and images of maps

Constructable loci

Algebraic properties : targes, fibers and source

Graded commutative algebra.

Notes:

Includes bibliographical references (pages 259-262) and indexes.

ISBN:

9782856298855

2856298850

OCLC:

1048929119