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020 $a9783319110295
024 7 $a10.1007/978-3-319-11029-5$2doi
040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng
082 04$a516.35$223
084 $aAMS 14-06
084 $aAMS 14F20
084 $aAMS 14G22
084 $aLC QA551
245 00$aBerkovich spaces and applications$h[electronic resource] /$cAntoine Ducros, Charles Favre, Johannes Nicaise, editors
260 $aCham [Switzerland] :$bSpringer,$c2015
300 $a1 online resource (xix, 413 pages)
440 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2119
504 $aIncludes bibliographical references
505 0 $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)
520 $aWe present an introduction to Berkovich?s theory of non-archimedean analytic spaces that emphasizes its applications in various fields. The first part contains surveys of a foundational nature, including an introduction to Berkovich analytic spaces by M. Temkin, and to étale cohomology by A. Ducros, as well as a short note by C. Favre on the topology of some Berkovich spaces. The second part focuses on applications to geometry. A second text by A. Ducros contains a new proof of the fact that the higher direct images of a coherent sheaf under a proper map are coherent, and B. Rémy, A. Thuillier and A. Werner provide an overview of their work on the compactification of Bruhat-Tits buildings using Berkovich analytic geometry. The third and final part explores the relationship between non-archimedean geometry and dynamics. A contribution by M. Jonsson contains a thorough discussion of non-archimedean dynamical systems in dimension 1 and 2. Finally a survey by J.-P. Otal gives an account of Morgan-Shalen's theory of compactification of character varieties. This book will provide the reader with enough material on the basic concepts and constructions related to Berkovich spaces to move on to more advanced research articles on the subject. We also hope that the applications presented here will inspire the reader to discover new settings where these beautiful and intricate objects might arise
650 0$aGeometry, Analytic
650 0$aTopology
700 1 $aDucros, Antoine$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0739650
700 1 $aFavre, Charles$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0478896
700 1 $aNicaise, Johannes$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0721075
776 08$aPrinted edition:$z9783319110288
856 40$uhttp://link.springer.com/book/10.1007/978-3-319-11029-5$zAn electronic book accessible through the World Wide Web
907 $a.b14258286$b14-07-16$c14-07-16
912 $ab1425828
945 $cE-book$g1$lle013$o-$pE0,00$q-$rn$so$t0$u0$v0$w0$x0$y.i15728365$z14-07-16
996 $aBerkovich spaces and applications$91465253
997 $aUNISALENTO
998 $ale013$b14-07-16$cm$d@$e-$feng$gsz $h0$i0