







1. 
Record Nr. 
UNISALENTOb1425828 


Titolo 
Berkovich spaces and applications [electronic resource] / Antoine Ducros, Charles Favre, Johannes Nicaise, editors 







Pubbl/distr/stampa 


Cham [Switzerland] : Springer, 2015 







ISBN 






Descrizione fisica 

1 online resource (xix, 413 pages) 






Collana 

Lecture Notes in Mathematics, 16179692 ; 2119 






Classificazione 

AMS 1406 
AMS 14F20 
AMS 14G22 
LC QA551 








Altri autori (Persone) 

Ducros, Antoineauthor 
Favre, Charlesauthor 
Nicaise, Johannesauthor 








Disciplina 






Soggetti 

Geometry, Analytic 
Topology 








Lingua di pubblicazione 






Formato 
Materiale a stampa 





Livello bibliografico 
Monografia 





Nota di bibliografia 

Includes bibliographical references 






Nota di contenuto 

Introduction to Berkovich analytic spaces  Etale cohomology of schemes and analytic spaces  Countability properties of Berkovich spaces  Cohomological finiteness of proper morphisms in algebraic geometry: a purely transcendental proof, without projective tools  BruhatTits buildings and analytic geometry  Dynamics on Berkovich spaces in low dimensions  Compactifications of spaces of representations (after Culler, Morgan and Shalen) 








Sommario/riassunto 

We present an introduction to Berkovich?s theory of nonarchimedean analytic spaces that emphasizes its applications in various fields. The first part contains surveys of a foundational nature, including an introduction to Berkovich analytic spaces by M. Temkin, and to étale cohomology by A. Ducros, as well as a short note by C. Favre on the topology of some Berkovich spaces. The second part focuses on applications to geometry. A second text by A. Ducros contains a new proof of the fact that the higher direct images of a coherent sheaf under a proper map are coherent, and B. Rémy, A. Thuillier and A. Werner provide an overview of their work on the compactification of 



