000 | 04217nam a22005895i 4500 | ||
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001 | 978-3-319-11029-5 | ||
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_a9783319110295 _9978-3-319-11029-5 |
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_a10.1007/978-3-319-11029-5 _2doi |
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_aPBMW _2bicssc |
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_aMAT012010 _2bisacsh |
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_aPBMW _2thema |
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_a516.35 _223 |
245 | 1 | 0 |
_aBerkovich Spaces and Applications _h[electronic resource] / _cedited by Antoine Ducros, Charles Favre, Johannes Nicaise. |
250 | _a1st ed. 2015. | ||
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2015. |
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300 |
_aXIX, 413 p. 18 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2119 |
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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 | _aAlgebraic geometry. | |
650 | 0 | _aDynamics. | |
650 | 0 | _aErgodic theory. | |
650 | 0 | _aTopological groups. | |
650 | 0 | _aLie groups. | |
650 | 1 | 4 |
_aAlgebraic Geometry. _0https://scigraph.springernature.com/ontologies/product-market-codes/M11019 |
650 | 2 | 4 |
_aDynamical Systems and Ergodic Theory. _0https://scigraph.springernature.com/ontologies/product-market-codes/M1204X |
650 | 2 | 4 |
_aTopological Groups, Lie Groups. _0https://scigraph.springernature.com/ontologies/product-market-codes/M11132 |
700 | 1 |
_aDucros, Antoine. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
|
700 | 1 |
_aFavre, Charles. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
|
700 | 1 |
_aNicaise, Johannes. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer Nature eBook | |
776 | 0 | 8 |
_iPrinted edition: _z9783319110301 |
776 | 0 | 8 |
_iPrinted edition: _z9783319110288 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2119 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-319-11029-5 |
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