Lectures on Formal and Rigid Geometry

AvSiegfried Bosch

Häftad, Engelska, 2014

Del 2105 i serien Lecture Notes in Mathematics

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Beskrivning

The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work.This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".

Produktinformation

Utgivningsdatum:2014-09-04
Mått:155 x 235 x 15 mm
Vikt:406 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:254
Upplaga:2014
Förlag:Springer International Publishing AG
ISBN:9783319044163

Utforska kategorier

Talteori inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Recensioner i media

"Its aim is to offer a rapid and mostly self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by Tate, together with the formal algebraic geometry approach set up by Raynaud. Furthermore, the volume provides enlightening examples of rigid spaces and points out analogies with and differences from the theory of schemes. The book is suitable for a first course on formal and rigid geometry, but it can be used equally well for personal study." (Alessandra Bertapelle, Mathematical Reviews, March, 2016) "All notions introduced are discussed thoroughly, proofs are lucid and elegant, and the hypotheses made and their relevance are clear throughout the text. ... The reader comes away from the text with a thorough understanding of the internal motivations of the theory of formal and rigid spaces. The book is an extremely readable introduction to its subject, as well as to the techniques of modern geometry in general." (Jeroen Sijsling, zbMATH 1314.14002, 2015)

Innehållsförteckning

Classical Rigid Geometry.- Tate Algebras.- Affinoid Algebras and their Associated Spaces.- Affinoid Functions.- Towards the Notion of Rigid Spaces.- Coherent Sheaves on Rigid Spaces.- Formal Geometry.- Adic Rings and their Associated Formal Schemes.- Raynaud's View on Rigid Spaces.- More Advanced Stuff.- Appendix.- References.- Index.