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|a Fresnel, Jean.
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1 |
0 |
|a Rigid analytic geometry and its applications /
|c Jean Fresnel, Marius van der Put.
|
| 264 |
|
1 |
|a Boston :
|b Birkhäuser,
|c [2004]
|
| 264 |
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4 |
|c ©2004
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| 300 |
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|a 1 online resource (xi, 296 pages)
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|b txt
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|2 rdamedia
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|a online resource
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| 490 |
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|a Progress in mathematics ;
|v v. 218
|
| 504 |
|
|
|a Includes bibliographical references (pages [275]-288) and index.
|
| 538 |
|
|
|a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
|u http://purl.oclc.org/DLF/benchrepro0212
|5 MiAaHDL
|
| 583 |
1 |
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|a digitized
|c 2010
|h HathiTrust Digital Library
|l committed to preserve
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|a Preface -- Valued fields and normed spaces -- The projective line -- Affinoid algebras -- Rigid spaces -- Curves and their reductions -- Abelian varieties -- Points of rigid spaces, rigid cohomology -- Etale cohomology of rigid spaces -- Covers of algebraic curves -- References -- List of Notation -- Index.
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| 520 |
|
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|a The theory of rigid (analytic) spaces, originally invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties, has undergone significant growth in the last two decades; today the theory has applications to arithmetic algebraic geometry, number theory, the arithmetic of function fields, and p-adic differential equations. This work, a revised and greatly expanded new English edition of the earlier French text by the same authors, is an accessible introduction to the theory of rigid spaces and now includes a large number of exercises. Key topics: - Chapters on the applications of this theory to curves and abelian varieties: the Tate curve, stable reduction for curves, Mumford curves, Néron models, uniformization of abelian varieties - Unified treatment of the concepts: points of a rigid space, overconvergent sheaves, Monsky--Washnitzer cohomology and rigid cohomology; detailed examination of Kedlaya's application of the Monsky--Washnitzer cohomology to counting points on a hyperelliptic curve over a finite field - The work of Drinfeld on "elliptic modules" and the Langlands conjectures for function fields use a background of rigid étale cohomology; detailed treatment of this topic - Presentation of the rigid analytic part of Raynaud's proof of the Abhyankar conjecture for the affine line, with only the rudiments of that theory A basic knowledge of algebraic geometry is a sufficient prerequisite for this text. Advanced graduate students and researchers in algebraic geometry, number theory, representation theory, and other areas of mathematics will benefit from the book's breadth and clarity.
|
| 588 |
|
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|a Description based on print version record.
|
| 500 |
|
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|a Electronic resource.
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| 650 |
|
0 |
|a Analytic spaces.
|
| 650 |
|
0 |
|a Geometry, Analytic.
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| 650 |
|
0 |
|a Geometry, Algebraic.
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| 650 |
|
6 |
|a Espaces analytiques.
|
| 650 |
|
6 |
|a Géométrie analytique.
|
| 650 |
|
6 |
|a Géométrie algébrique.
|
| 650 |
|
7 |
|a Analytic spaces.
|2 fast
|0 (OCoLC)fst00808342
|
| 650 |
|
7 |
|a Geometry, Algebraic.
|2 fast
|0 (OCoLC)fst00940902
|
| 650 |
|
7 |
|a Geometry, Analytic.
|2 fast
|0 (OCoLC)fst00940905
|
| 650 |
|
7 |
|a Geometria algebrica.
|2 larpcal
|
| 650 |
|
7 |
|a Espaces analytiques.
|2 ram
|
| 650 |
|
7 |
|a Géométrie analytique.
|2 ram
|
| 650 |
|
7 |
|a Géométrie algébrique.
|2 ram
|
| 650 |
0 |
7 |
|a Rigid-analytischer Raum.
|2 swd
|
| 650 |
0 |
7 |
|a Analytische Geometrie.
|2 swd
|
| 655 |
|
7 |
|a Electronic books.
|2 local
|
| 700 |
1 |
|
|a Put, Marius van der,
|d 1941-
|
| 710 |
2 |
|
|a SpringerLink (Online service)
|
| 776 |
1 |
8 |
|i Print version:
|a Fresnel, Jean.
|t Rigid analytic geometry and its applications.
|d Boston : Birkhäuser, ©2004
|w (DLC) 2003051895
|w (OCoLC)52216244
|
| 830 |
|
0 |
|a Progress in mathematics (Boston, Mass.) ;
|v v. 218.
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| 856 |
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|a Texas A&M University
|b College Station
|c Electronic Resources
|d Available Online
|t 0
|e QA331 .F7765 2004
|h Library of Congress classification
|
| 998 |
f |
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|a QA331 .F7765 2004
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|l Available Online
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