Lectures on Formal and Rigid Geometry
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Beschreibung
A first version of this work appeared in 2005 as a Preprint of the Collaborative Research Center "Geometrical Structures in Mathematics" at the University of Münster. Its aim was 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 the original preprint and has been published at the suggestion of several experts in the field.
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".
Provides rapid access to advanced Rigid Geometry Offers self-contained content Includes Tate’s classical theory, as well as Raynaud’s approach using formal schemes
Autor*in
Siegfried Bosch
Themen in »Lectures on Formal and Rigid Geometry«
Formal blowing-up Formal scheme Rigid analytic space Tate algebra Tate's Acyclicity Theorem
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“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 bookis an extremely readable introduction to its subject, as well as to the techniques of modern geometry in general.” (Jeroen Sijsling, zbMATH 1314.14002, 2015)
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