Rigid Analytic Geometry and its Applications

Name: Rigid Analytic Geometry and its Applications
Brand: Birkhäuser
SKU: 9780817642068
Price: 2234 CZK
Availability: InStock

Autor: Jean Fresnel, Marius van der Put

Jazyk:

Vazba: Pevná

Vydavatel: Birkhäuser

Dostupnost: Skladem u dodavatele

Odesíláme za 10-13 dnů

2 234 Kč

The theory of rigid (analytic) spaces, originally invented to describe degenerations, reductions, an...

Informace o knize

Autor

Jean Fresnel, Marius van der Put

Jazyk

Angličtina

Vazba

Kniha - Pevná

Vydáno

2003

Stránek

299

EAN

9780817642068

ISBN

0817642064

Enbook ID

01399296

Vydavatel

Birkhäuser

Hmotnost

578

Rozměry

166 x 243 x 21

Kompletní popis

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, 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.

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