Lectures on Formal and Rigid Geometry

✍ Scribed by Siegfried Bosch (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 255
• Series: Lecture Notes in Mathematics 2105
• Edition: 1
• Category: Library

✦ Synopsis

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".

✦ Table of Contents

Front Matter....Pages i-viii
Introduction....Pages 1-5
Front Matter....Pages 7-7
Tate Algebras....Pages 9-29
Affinoid Algebras and Their Associated Spaces....Pages 31-63
Affinoid Functions....Pages 65-91
Towards the Notion of Rigid Spaces....Pages 93-116
Coherent Sheaves on Rigid Spaces....Pages 117-147
Front Matter....Pages 149-149
Adic Rings and Their Associated Formal Schemes....Pages 151-173
Raynaud’s View on Rigid Spaces....Pages 175-214
More Advanced Stuff....Pages 215-227
Back Matter....Pages 229-256

✦ Subjects

Mathematics, general; Algebraic Geometry; Number Theory