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 

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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. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL 

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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 padic 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, MonskyWashnitzer cohomology and rigid cohomology; detailed examination of Kedlaya's application of the MonskyWashnitzer 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


Rigidanalytischer 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

