An edition of Families of Berkovich spaces (2018)

Families of Berkovich spaces

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Families of Berkovich spaces
Antoine Ducros, Antoine Ducros
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Last edited by MARC Bot
December 17, 2022 | History
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An edition of Families of Berkovich spaces (2018)

Families of Berkovich spaces

by

"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.

Publish Date
Publisher
Société mathématique de France
Language
English
Pages
262

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Subjects

Analytic spaces, Zariski surfaces, Arithmetical algebraic geometry

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Edition Availability
Cover of: Families of Berkovich spaces
Families of Berkovich spaces
2018, Société mathématique de France
in English
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Book Details

Table of 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.

Edition Notes

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

In English. Abstract in English and French.

Published in
Paris
Series
Astérisque -- 400, Astérisque -- 400.
Copyright Date
2018

Classifications

Library of Congress
QA331 .D83 2018, QA1 .A85 no. 400

The Physical Object

Pagination
vii, 262 pages
Number of pages
262

ID Numbers

Open Library
OL44198154M
ISBN 10
2856298850
ISBN 13
9782856298855
OCLC/WorldCat
1048929119

Source records

marc_columbia MARC record

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December 17, 2022 Created by MARC Bot Imported from marc_columbia MARC record