TY  - BOOK
AU  - Ducros,Antoine
TI  - Families of Berkovich spaces
T2  - Asterisque,
SN  - 9782856298855
U1  - 510=4 23
PY  - 2018///
CY  - Paris :  
PB  - Societe mathematique de France,  
KW  - Analytic spaces
KW  - Zariski surfaces
KW  - Arithmetical algebraic geometry
N1  - 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
N2  - 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
ER  -