Six lectures on commutative algebra

Interest in commutative algebra has surged over the past decades. In order tosurvey and highlight recent developments in this rapidly expanding field, theCentre de Recerca Matematica in Bellaterra organized a ten-days Summer Schoolon 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 thenovice 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 paperis 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, hehas 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 tocompute them.' - Zentralblatt MATH" Synthesis of lectures in a Summer School given at the Centre de Recerca Matematica in Bellaterra (Spain) Fresh and extensive account of the results, techniques and problems of some of the most active areas of research INDICE: Preface.- Infinite Free Resolutions.- Generic Initial Ideals.- Tight Closure, Parameter Ideals, and Geometry.- On the Use of Local Cohomology inAlgebra and Geometry.- Problems and Results on Hilbert Functions of Graded Algebras.- Cohomological Degrees of Graded Modules.

• ISBN: 978-3-0346-0328-7
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 412
• Fecha Publicación: 01/12/2009
• Nº Volúmenes: 1
• Idioma: Inglés