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作者 Fresnel, Jean
書名 Rigid analytic geometry and its applications [electronic resource] / Jean Fresnel, Marius van der Put
出版項 Boston : Birkhäuser, ©2004
國際標準書號 9781461200413 (electronic bk.)
1461200415 (electronic bk.)
book jacket
說明 1 online resource (xi, 296 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Progress in mathematics ; v. 218
Progress in mathematics (Boston, Mass.) ; v. 218
附註 Includes bibliographical references (p. [275]-288) and index
Use copy Restrictions unspecified star MiAaHDL
Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
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. MiAaHDL
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
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
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
Description based on print version record
鏈接 Print version: Fresnel, Jean. Rigid analytic geometry and its applications. Boston : Birkhäuser, ©2004 (DLC) 2003051895 (OCoLC)52216244
主題 Analytic spaces
Geometry, Analytic
Geometry, Algebraic
Espaces analytiques
Géométrie analytique
Géométrie algébrique
Geometria algébrica. larpcal
Espaces analytiques. ram
Géométrie analytique. ram
Géométrie algébrique. ram
Rigid-analytischer Raum. swd
Analytische Geometrie. swd
Analytic spaces. fast (OCoLC)fst00808342
Geometry, Algebraic. fast (OCoLC)fst00940902
Geometry, Analytic. fast (OCoLC)fst00940905
Electronic books
Alt Author Put, Marius van der, 1941-
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