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Families of Berkovich Spaces
 
Antoine Ducros Sorbonne Université, Paris, France
A publication of the Société Mathématique de France
Families of Berkovich Spaces
Softcover ISBN:  978-2-85629-885-5
Product Code:  AST/400
List Price: $75.00
AMS Member Price: $60.00
Please note AMS points can not be used for this product
Families of Berkovich Spaces
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Families of Berkovich Spaces
Antoine Ducros Sorbonne Université, Paris, France
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-885-5
Product Code:  AST/400
List Price: $75.00
AMS Member Price: $60.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    Astérisque
    Volume: 4002018; 262 pp
    MSC: Primary 14

    This book investigates the variation of the properties of the fibers of a map between analytic spaces in the sense of Berkovich. First, the author studies flatness in this setting; the naive definition of this notion is not reasonable and he explains why. He then describes the loci of fiberwise validity of some usual properties (e.g., Cohen-Macaulay, Gorenstein, geometrically regular). He shows that these are (locally) Zariski-constructible subsets of the source space. For that purpose, he develops systematic methods for “spreading out” in Berkovich geometry, as is done in scheme theory, some properties from a generic fiber to a neighborhood of it.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians interested in Berkovich spaces.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 4002018; 262 pp
MSC: Primary 14

This book investigates the variation of the properties of the fibers of a map between analytic spaces in the sense of Berkovich. First, the author studies flatness in this setting; the naive definition of this notion is not reasonable and he explains why. He then describes the loci of fiberwise validity of some usual properties (e.g., Cohen-Macaulay, Gorenstein, geometrically regular). He shows that these are (locally) Zariski-constructible subsets of the source space. For that purpose, he develops systematic methods for “spreading out” in Berkovich geometry, as is done in scheme theory, some properties from a generic fiber to a neighborhood of it.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in Berkovich spaces.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.