E-Book Overview
This book is based on lectures by six internationally known experts presented at the 2002 MSRI introductory workshop on commutative algebra. They focus on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics, with all necessary background provided. Short complementary papers describing work at the research frontier are also included. The unusual scope and format make the book invaluable reading for graduate students and researchers interested in commutative algebra and its various uses.
E-Book Content
This book is based on expository lectures by six internationally known experts presented at the 2002 MSRI introductory workshop on commutative algebra. They focus on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics, with all necessary background provided. Short complementary papers describing work at the research frontier are also included. The unusual scope and format make the book invaluable reading for graduate students and researchers interested in commutative algebra and its various uses. Mathematical Sciences Research Institute Publications 51 Trends in Commutative Algebra Mathematical Sciences Research Institute Publications 1 2 3 4 5 6 7 8 9 10–11 12–13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 Freed/Uhlenbeck: Instantons and Four-Manifolds, second edition Chern (ed.): Seminar on Nonlinear Partial Differential Equations Lepowsky/Mandelstam/Singer (eds.): Vertex Operators in Mathematics and Physics Kac (ed.): Infinite Dimensional Groups with Applications Blackadar: K-Theory for Operator Algebras, second edition Moore (ed.): Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics Chorin/Majda (eds.): Wave Motion: Theory, Modelling, and Computation Gersten (ed.): Essays in Group Theory Moore/Schochet: Global Analysis on Foliated Spaces Drasin/Earle/Gehring/Kra/Marden (eds.): Holomorphic Functions and Moduli Ni/Peletier/Serrin (eds.): Nonlinear Diffusion Equations and Their Equilibrium States Goodman/de la Harpe/Jones: Coxeter Graphs and Towers of Algebras Hochster/Huneke/Sally (eds.): Commutative Algebra Ihara/Ribet/Serre (eds.): Galois Groups over Q Concus/Finn/Hoffman (eds.): Geometric Analysis and Computer Graphics Bryant/Chern/Gardner/Goldschmidt/Griffiths: Exterior Differential Systems Alperin (ed.): Arboreal Group Theory Dazord/Weinstein (eds.): Symplectic Geometry, Groupoids, and Integrable Systems Moschovakis (ed.): Logic from Computer Science Ratiu (ed.): The Geometry of Hamiltonian Systems Baumslag/Miller (eds.): Algorithms and Classification in Combinatorial Group Theory Montgomery/Small (eds.): Noncommutative Rings Akbulut/King: Topology of Real Algebraic Sets Judah/Just/Woodin (eds.): Set Theory of the Continuum Carlsson/Cohen/Hsiang/Jones (eds.): Algebraic Topology and Its Applications Clemens/Koll´ ar (eds.): Current Topics in Complex Algebraic Geometry Nowakowski (ed.): Games of No Chance Grove/Petersen (eds.): Comparison Geometry Levy (ed.): Flavors of Geometry Cecil/Chern (eds.): Tight and Taut Submanifolds Axler/McCarthy/Sarason (eds.): Holomorphic Spaces Ball/Milman (eds.): Convex Geometric Analysis Levy (ed.): The Eightfold Way Gavosto/Krantz/McCallum (eds.): Contemporary Issues in Mathematics Education Schneider/Siu (eds.): Several Complex Variables Billera/Bj¨ orner/Green/Simion/Stanley (eds.): New Perspectives in Geometric Combinatorics Haskell/Pillay/Steinhorn (eds.): Model Theory, Algebra, and Geometry Bleher/Its (eds.): Random Matrix Models and Their Applications Schneps (ed.): Galois Groups and Fundamental Groups Nowakowski (ed.): More Ga