03252cam a2200349 i 4500008004100000020001800041024003500059040006600094082001500160084001400175084001400189084001400203084001300217245009800230260004200328300003300370440005300403504004000456505045200496520141400948650002302362650001302385700007902398700007802477700008102555907003502636912001302671945011102684996004702795997001502842998004502857160714s2015 sz a ob 000 0 eng d a97833191102887 a10.1007/978-3-319-11029-52doi aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicabeng04a516.35223 aAMS 14-06 aAMS 14F20 aAMS 14G22 aLC QA55100aBerkovich spaces and applications /cAntoine Ducros, Charles Favre, Johannes Nicaise, editors aCham [Switzerland] :bSpringer,c2015 axix, 413 p. :bill. ;c24 cm 0aLecture notes in mathematics,x0075-8434 ;v2119 aIncludes bibliographical references0 aIntroduction 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 -- Bruhat-Tits buildings and analytic geometry -- Dynamics on Berkovich spaces in low dimensions -- Compactifications of spaces of representations (after Culler, Morgan and Shalen) aWe present an introduction to Berkovich?s theory of non-archimedean 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 Bruhat-Tits buildings using Berkovich analytic geometry. The third and final part explores the relationship between non-archimedean geometry and dynamics. A contribution by M. Jonsson contains a thorough discussion of non-archimedean dynamical systems in dimension 1 and 2. Finally a survey by J.-P. Otal gives an account of Morgan-Shalen's theory of compactification of character varieties. This book will provide the reader with enough material on the basic concepts and constructions related to Berkovich spaces to move on to more advanced research articles on the subject. We also hope that the applications presented here will inspire the reader to discover new settings where these beautiful and intricate objects might arise 0aGeometry, Analytic 0aTopology1 aDucros, Antoineeauthor4http://id.loc.gov/vocabulary/relators/aut07396501 aFavre, Charleseauthor4http://id.loc.gov/vocabulary/relators/aut04788961 aNicaise, Johanneseauthor4http://id.loc.gov/vocabulary/relators/aut0721075 a.b14258298b22-11-16c14-07-16 ab1425829 aLE013 14-XX DUC11 (2015)g1i2013000293691lle013oppE72,79q-rls-t0u1v0w1x0y.i15788799z22-11-16 aBerkovich spaces and applications91465253 aUNISALENTO ale013b14-07-16cmdae-fenggsz h0i0