LEADER 04566nam 22007575 450 001 996202187503316 005 20200701094157.0 010 $a3-319-11029-2 024 7 $a10.1007/978-3-319-11029-5 035 $a(CKB)3710000000306122 035 $a(SSID)ssj0001386365 035 $a(PQKBManifestationID)11798994 035 $a(PQKBTitleCode)TC0001386365 035 $a(PQKBWorkID)11373896 035 $a(PQKB)10868703 035 $a(DE-He213)978-3-319-11029-5 035 $a(MiAaPQ)EBC6286439 035 $a(MiAaPQ)EBC5586934 035 $a(Au-PeEL)EBL5586934 035 $a(OCoLC)1066181540 035 $a(PPN)183094360 035 $a(EXLCZ)993710000000306122 100 $a20141121d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBerkovich Spaces and Applications$b[electronic resource] /$fedited by Antoine Ducros, Charles Favre, Johannes Nicaise 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XIX, 413 p. 18 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2119 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-11028-4 320 $aIncludes bibliographical references. 327 $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). 330 $aWe present an introduction to Berkovich?s theory of non-archimedean analytic spaces that emphasizes its applications in various fields. The first part contains surveys of a foundational nature, including an introduction to Berkovich analytic spaces by M. Temkin, and to étale cohomology by A. Ducros, as well as a short note by C. Favre on the topology of some Berkovich spaces. The second part focuses on applications to geometry. A second text by A. Ducros contains a new proof of the fact that the higher direct images of a coherent sheaf under a proper map are coherent, and B. Rémy, A. Thuillier and A. Werner provide an overview of their work on the compactification of Bruhat-Tits buildings using Berkovich analytic geometry. The third and final part explores the relationship between non-archimedean geometry and dynamics. A contribution by M. Jonsson contains a thorough discussion of non-archimedean dynamical systems in dimension 1 and 2. Finally a survey by J.-P. Otal gives an account of Morgan-Shalen's theory of compactification of character varieties. This book will provide the reader with enough material on the basic concepts and constructions related to Berkovich spaces to move on to more advanced research articles on the subject. We also hope that the applications presented here will inspire the reader to discover new settings where these beautiful and intricate objects might arise. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2119 606 $aAlgebraic geometry 606 $aDynamics 606 $aErgodic theory 606 $aTopological groups 606 $aLie groups 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 615 0$aAlgebraic geometry. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aTopological groups. 615 0$aLie groups. 615 14$aAlgebraic Geometry. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aTopological Groups, Lie Groups. 676 $a516.3 702 $aDucros$b Antoine$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aFavre$b Charles$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aNicaise$b Johannes$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996202187503316 996 $aBerkovich spaces and applications$91387924 997 $aUNISA