Softcover ISBN: | 978-2-85629-885-5 |
Product Code: | AST/400 |
List Price: | $75.00 |
AMS Member Price: | $60.00 |
Softcover ISBN: | 978-2-85629-885-5 |
Product Code: | AST/400 |
List Price: | $75.00 |
AMS Member Price: | $60.00 |
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Book DetailsAstérisqueVolume: 400; 2018; 262 ppMSC: 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.
ReadershipGraduate students and research mathematicians interested in Berkovich spaces.
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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.
Graduate students and research mathematicians interested in Berkovich spaces.