Six lectures on commutative algebra
著者
書誌事項
Six lectures on commutative algebra
（Modern Birkhäuser classics）
Birkhäuser, c2010
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注記
"Reprint of the 1998 edition."
"Originally published under the same title as volume 166 in the Progress in mathematics series by Birkhäuser Verlag, ... c1998 ..."--T.p. verso
Contains texts grown out of the six series of lectures given by the authors in the Summer School on Commutative Algebra held from July 16 to 26, 1996, at the Centre de recerca matemàtica (CRM) in Bellaterra
内容説明・目次
内容説明
Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it.
Reviews
"All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum
Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews
Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH
Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH
Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews
Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH
目次
Infinite Free Resolutions.- Generic Initial Ideals.- Tight Closure, Parameter Ideals, and Geometry.- On the Use of Local Cohomology in Algebra and Geometry.- Problems and Results on Hilbert Functions of Graded Algebras.- Cohomological Degrees of Graded Modules.
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