skip to content
Families of Berkovich spaces Preview this item
ClosePreview this item
Checking...

Families of Berkovich spaces

Author: Antoine Ducros
Publisher: Paris : Société mathématique de France, 2018. ©2018
Series: Astérisque, 400.
Edition/Format:   Print book : EnglishView all editions and formats
Publication:Astérisque, no:400
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  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Document Type: Book
All Authors / Contributors: Antoine Ducros
ISBN: 9782856298855 2856298850
OCLC Number: 1048929119
Language Note: In English. Abstract in English and French.
Description: vii, 262 pages : illustrations ; 24 cm.
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.
Series Title: Astérisque, 400.
Responsibility: Antoine Ducros.

Abstract:

"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.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/1048929119> # Families of Berkovich spaces
    a schema:Book, schema:CreativeWork ;
    library:oclcnum "1048929119" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/fr> ;
    schema:about <http://dewey.info/class/515.942/e23/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/5449087755#Topic/zariski_surfaces> ; # Zariski surfaces
    schema:about <http://experiment.worldcat.org/entity/work/data/5449087755#Topic/31_51_algebraic_geometry> ; # 31.51 algebraic geometry
    schema:about <http://experiment.worldcat.org/entity/work/data/5449087755#Topic/arithmetical_algebraic_geometry> ; # Arithmetical algebraic geometry
    schema:about <http://experiment.worldcat.org/entity/work/data/5449087755#Topic/analytic_spaces> ; # Analytic spaces
    schema:author <http://experiment.worldcat.org/entity/work/data/5449087755#Person/ducros_antoine> ; # Antoine Ducros
    schema:bookFormat bgn:PrintBook ;
    schema:copyrightYear "2018" ;
    schema:datePublished "2018" ;
    schema: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."@en ;
    schema:description "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."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/5449087755> ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://worldcat.org/issn/0303-1179> ; # Astérisque,
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/5449087755#Series/asterisque> ; # Astérisque ;
    schema:name "Families of Berkovich spaces"@en ;
    schema:productID "1048929119" ;
    schema:workExample <http://worldcat.org/isbn/9782856298855> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/1048929119> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/5449087755#Person/ducros_antoine> # Antoine Ducros
    a schema:Person ;
    schema:familyName "Ducros" ;
    schema:givenName "Antoine" ;
    schema:name "Antoine Ducros" ;
    .

<http://experiment.worldcat.org/entity/work/data/5449087755#Series/asterisque> # Astérisque ;
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/1048929119> ; # Families of Berkovich spaces
    schema:name "Astérisque ;" ;
    .

<http://experiment.worldcat.org/entity/work/data/5449087755#Topic/31_51_algebraic_geometry> # 31.51 algebraic geometry
    a schema:Intangible ;
    schema:name "31.51 algebraic geometry"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/5449087755#Topic/arithmetical_algebraic_geometry> # Arithmetical algebraic geometry
    a schema:Intangible ;
    schema:name "Arithmetical algebraic geometry"@en ;
    .

<http://worldcat.org/isbn/9782856298855>
    a schema:ProductModel ;
    schema:isbn "2856298850" ;
    schema:isbn "9782856298855" ;
    .

<http://worldcat.org/issn/0303-1179> # Astérisque,
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/1048929119> ; # Families of Berkovich spaces
    schema:issn "0303-1179" ;
    schema:name "Astérisque," ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.