TAILIEUCHUNG - Smoothness, Regularity and Complete Intersection

This book proves a number of important theorems that are commonly given in advanced books on Commutative Algebra without proof, owing to the difficulty of the existing proofs. In short, we give homological proofs of these results, but instead of the original ones involving simplicial methods, we modify these to use only lower dimensional homology modules, that we can introduce in an ad hoc way, thus avoiding simplicial theory. This allows us to give complete and comparatively short proofs of the important results we state below. We hope these notes can serve as a complement to the existing literature | 373 London Mathematical Society Lecture Note Series Smoothness Regularity and Complete Intersection Javier Majadas and Antonio G. Rodicio Cambridge The London Mathematical Society Cambridge more information - 9780521125727 This page intentionally left blank LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES Managing Editor Professor M. Reid Mathematics Institute University ofWarwick Coventry CV4 7AL United Kingdom The titles below are available from booksellers or from Cambridge University Press at mathematics 222 Advances in linear logic GIRARD Y LAFONT L. REGNIER eds 223 Analytic semigroups and semilinear initial boundary value problems K. TAIRA 224 Computability enumerability unsolvability . COOPER . SLAMAN eds 225 A mathematical introduction to string theory etal 226 Novikov conjectures index theorems andrigidity I . FERRY A. RANICKI J. ROSENBERG eds 227 Novikov conjectures index theorems and rigidity II . FERRY A. RANICKI J. ROSENBERG eds 228 Ergodic theory of Zd-actions M. POLLICOTT K. SCHMIDT eds 229 Ergodicity for infinite dimensional systems G. DA PRATO J. ZABCZYK 230 Prolegomena to a middlebrow arithmetic of curves of genus 2 . CASSELS . FLYNN 231 Semigroup theory and its applications . HOFMANN . MISLOVE eds 232 Thedescriptive set theory ofPolishgroup actions H. BECKER . KECHRIS 233 Finite fields and applications S. COHEN H. NIEDERREITER eds 234 Introduction to subfactors V. JONES . SUNDER 235 Number theory Séminairedethéoriedes nombres deParis 1993-94 ed 236 The James forest H. FETTER B. GAMBOA DE BUEN 237 Sieve methods exponential sums and their applications in number theory . GREAVES et al eds 238 Representation theory and algebraic geometry A. MARTSINKOVSKY G. TODOROV eds 240 Stable groups . WAGNER 241 Surveys in combinatorics 1997 . BAILEY ed 242 Geometric Galois actions I L. SCHNEPS P. LOCHAK eds 243 Geometric Galois actions II L. SCHNEPS

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