Title | Almost Ring Theory [electronic resource] |
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Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2003 |

Connect to | http://dx.doi.org/10.1007/b10047 |

Descript | VI, 318 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Algebra
Algebraic geometry
Category theory (Mathematics)
Homological algebra
Commutative algebra
Commutative rings
Field theory (Physics)
Mathematics
Algebra
Commutative Rings and Algebras
Algebraic Geometry
Category Theory Homological Algebra
Field Theory and Polynomials