Families of Berkovich spaces / Antoine Ducros.
Material type:
TextLanguage: English Summary language: English, French Series: Asterisque ; 400. | Astérisque ; 400.Publication details: Paris : Societe mathematique de France, 2018.Description: vii, 262 pages : illustrations ; 24 cmISBN: - 9782856298855
- 510=4 23 As853
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 510=4 As853 (Browse shelf(Opens below)) | Checked out | 08/11/2019 | C26641 |
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Includes bibliographical references and indexes.
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.
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.
Abstract also in French.
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