Almost Ring Theory - Ofer Gabber, Lorenzo Ramero

Almost Ring Theory

Buch | Softcover
VI, 318 Seiten
2003 | 2003
Springer Berlin (Verlag)
978-3-540-40594-8 (ISBN)
74,89 inkl. MwSt

This book develops thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring". Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions.

The reader is assumed to be familiar with general categorical notions, some basic commutative algebra and some advanced homological algebra (derived categories, simplicial methods). Apart from these general prerequisites, the text is as self-contained as possible. One novel feature of the book - compared with Faltings' earlier treatment - is the systematic exploitation of the cotangent complex, especially for the study of deformations of almost algebras.

From the content:

- Introduction
- Homological Theory
- Almost Ring Theory
- Fine Study of Almost Projective Modules
- Henselian Pairs
- Valuation Theory
- Analytic Geometry
- Appendix
- References
- Index

Erscheint lt. Verlag 11.8.2003
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo VI, 318 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 475 g
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte Algebra • Almost rings • deformations • Homological algebra • rigid geometry • Ring (Mathematik) • Ring Theory • valuations
ISBN-10 3-540-40594-1 / 3540405941
ISBN-13 978-3-540-40594-8 / 9783540405948
Zustand Neuware
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