Lectures on Formal and Rigid Geometry
Bosch, Siegfried.
Lectures on Formal and Rigid Geometry [electronic resource] / by Siegfried Bosch. - VIII, 254 p. online resource. - Lecture Notes in Mathematics, 2105 0075-8434 ; . - Lecture Notes in Mathematics, 2105 .
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.
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.
9783319044170
10.1007/978-3-319-04417-0 doi
Mathematics.
Geometry, algebraic.
Number theory.
Mathematics, general.
Algebraic Geometry.
Number Theory.
QA1-939
510
Lectures on Formal and Rigid Geometry [electronic resource] / by Siegfried Bosch. - VIII, 254 p. online resource. - Lecture Notes in Mathematics, 2105 0075-8434 ; . - Lecture Notes in Mathematics, 2105 .
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.
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.
9783319044170
10.1007/978-3-319-04417-0 doi
Mathematics.
Geometry, algebraic.
Number theory.
Mathematics, general.
Algebraic Geometry.
Number Theory.
QA1-939
510