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Rigid Analytic Geometry and Its Applications by Jean Fresnel (English) Paperback
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Item specifics
- Condition
- ISBN-13
- 9781461265856
- Book Title
- Rigid Analytic Geometry and Its Applications
- ISBN
- 9781461265856
- Subject Area
- Mathematics
- Publication Name
- Rigid Analytic Geometry and Its Applications
- Publisher
- Birkhäuser Boston
- Item Length
- 9.3 in
- Subject
- Geometry / General, Geometry / Algebraic, Mathematical Analysis
- Publication Year
- 2012
- Series
- Progress in Mathematics Ser.
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Weight
- 17.1 Oz
- Item Width
- 6.1 in
- Number of Pages
- Xi, 299 Pages
About this product
Product Information
Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.
Product Identifiers
Publisher
Birkhäuser Boston
ISBN-10
1461265851
ISBN-13
9781461265856
eBay Product ID (ePID)
202472902
Product Key Features
Number of Pages
Xi, 299 Pages
Language
English
Publication Name
Rigid Analytic Geometry and Its Applications
Publication Year
2012
Subject
Geometry / General, Geometry / Algebraic, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Series
Progress in Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Weight
17.1 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
Dewey Edition
21
Reviews
"... beginners will appreciate the numerous exercises and the gentle progression of the first four chapters, from the one-variable calculus on the projective line, through the algebraic study of general affinoid algebras, to the definition of general rigid varieties and their analytic reductions. And each of the last five chapters can be used as the basis for a student workshop at the advanced graduate level." --Mathematical Reviews "When I was a graduate student, we used the original (French) version of this book in an informal seminar on rigid geometry. It was quite helpful then, and it is much better now. The authors have updated the material, added quite a bit on new applications and new results, and changed languages. Despite the competition it now has, this is still one of the best places in which to start learning this theory." --MAA Reviews "The book under review gives a very complete and careful introduction into the technical foundations of the theory and also treats in detail the rigid analytic part of some of the important applications which the theory has found in recent years in number theory and geometry. The exposition is self contained, the authors only assume some familarity with basic algebraic geometry. . . Many of the subjects treated in this book are not easily available from the literature. The book which contains an extensive bibliography is a very valuable source for everyone wishing to learn about rigid geometry or its applications." ---Monatshefte für Mathematik, "... beginners will appreciate the numerous exercises and the gentle progression of the first four chapters, from the one-variable calculus on the projective line, through the algebraic study of general affinoid algebras, to the definition of general rigid varieties and their analytic reductions. And each of the last five chapters can be used as the basis for a student workshop at the advanced graduate level." --Mathematical Reviews "When I was a graduate student, we used the original (French) version of this book in an informal seminar on rigid geometry. It was quite helpful then, and it is much better now. The authors have updated the material, added quite a bit on new applications and new results, and changed languages. Despite the competition it now has, this is still one of the best places in which to start learning this theory." --MAA Reviews "The book under review gives a very complete and careful introduction into the technical foundations of the theory and also treats in detail the rigid analytic part of some of the important applications which the theory has found in recent years in number theory and geometry. The exposition is self contained, the authors only assume some familarity with basic algebraic geometry. . . Many of the subjects treated in this book are not easily available from the literature. The book which contains an extensive bibliography is a very valuable source for everyone wishing to learn about rigid geometry or its applications." ---Monatshefte fr Mathematik
Series Volume Number
218
Number of Volumes
1 Vol.
Illustrated
Yes
Dewey Decimal
516.3
Lc Classification Number
Qa440-699
Table of Content
1 Valued Fields and Normed Spaces.- 1.1 Valued fields.- 1.2 Banach spaces and Banach algebras.- 2 The Projective Line.- 2.1 Some definitions.- 2.2 Holomorphic functions on an affinoid subset.- 2.3 The residue theorem.- 2.4 The Grothendieck topology on P.- 2.5 Some sheaves on P.- 2.6 Analytic subspaces of P.- 2.7 Cohomology on an analytic subspace of P.- 3 Affinoid Algebras.- 3.1 Definition of an affinoid algebra.- 3.2 Consequences of the Weierstrass theorem.- 3.3 Affinoid spaces, Examples.- 3.4 Properties of the spectral (semi-)norm.- 3.5 Integral extensions of affinoid algebras.- 3.6 The differential module ?A/kf.- 3.7 Products of affinoid spaces, Picard groups.- 4 Rigid Spaces.- 4.1 Rational subsets.- 4.2 The weak G-topology and Tate's theorem.- 4.3 General rigid spaces.- 4.4 Sheaves on a rigid space.- 4.5 Coherent analytic sheaves.- 4.6 The sheaf of meromorphic functions.- 4.7 Rigid vector bundles.- 4.8 Analytic reductions and formal schemes.- 4.9 Analytic reductions of a subspace of Pk1, an.- 4.10 Separated and proper rigid spaces.- 5 Curves and Their Reductions.- 5.1 The Tate curve.- 5.2 Néron models for abelian varieties.- 5.3 The Néron model of an elliptic curve.- 5.4 Mumford curves and Schottky groups.- 5.5 Stable reduction of curves.- 5.6 A rigid proof of stable reduction for curves.- 5.7 The universal analytic covering of a curve.- 6 Abelian Varieties.- 6.1 The complex case.- 6.2 The non-archimedean case.- 6.3 The analytification of an algebraic torus.- 6.4 Lattices and analytic tori.- 6.5 Meromorphic functions on an analytic torus.- 6.6 Analytic tori and abelian varieties.- 6.7 Néron models and uniformization.- 7 Points of Rigid Spaces, Rigid Cohomology.- 7.1 Points and sheaves on an affinoid space.- 7.2 Explicit examples in dimension 1.- 7.3$$\mathcal{P}$$(X) and the reductions of X.- 7.4 Base change for overconvergent sheaves.- 7.5 Overconvergent affinoid spaces.- 7.6 Monsky-Washnitzer cohomology.- 7.7 Rigid cohomology.- 8 Etale Cohomology of Rigid Spaces.- 8.1 Etale morphisms.- 8.2 The étale site.- 8.3 Etale points, overconvergent étale sheaves.- 8.4 Etale cohomology in dimension 1.- 8.5 Higher dimensional rigid spaces.- 9 Covers of Algebraic Curves.- 9.1 Introducing the problem.- 9.2 I. Serre's result.- 9.3 II. Rigid construction of coverings.- 9.4 III. Reductions of curves modulo p.- References.- List of Notation.
Copyright Date
2004
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