Title Representation theory and algebraic geometry / edited by A. Martsinkovsky, G. Todorov

Published Cambridge, UK ; New York : Cambridge University Press, 1997

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Description 1 online resource (123 pages) Series London Mathematical Society lecture note series ; 238 London Mathematical Society lecture note series ; 238. Contents Cover; Title; Copyright; Contents; Preface; Some problems on three-dimensional graded domains; 1. Introduction.; 2. Examples of graded domains of GK-dimension 3.; 3. A General Description of X = Proj A.; 4. A Conjecture.; 5. The Division Rings.; 6. Evidence.; 7. Prime Divisors of the Sklyanin Division Ring:; 8. Deformation of a Commutative Surface.; 9. An example of noncommutative blowing up.; References.; The mathematical influence of Maurice Auslander in Mexico; 1. Almost split sequences and irreducible maps.; 2. Powers of Dtr.; 3. Almost split sequences in subcategories 4. Stable equivalence.5. The influence of M. Auslander in the development of representation theory in Mexico.; References; Intertwined with Maurice; REFERENCES; Introduction to Koszul Algebras; Abstract; 1 Introduction and Definitions; 2 Fundamental Theorems on Koszul Algebras; 3 Fundamental Results on Koszul Modules; 4 The Nongraded Case; 5 Global Dimensions 1 and 2 and Auslander Algebras; 6 Grobner Bases and Koszul Algebras; 7 Generalized Preprojective Algebras; References; Old and recent work with Maurice; 1 Stable equivalence; 2 Almost split sequences; 3 Commutative rings 4 Tilting theory5 Contravariantly finite subcategories and syzygies; References; The development of the representation theory of finite dimensional algebras 1968-1975; The Setting; Eight Topics in Eight Years; The Representation Types; The Basic Concepts; Seven Plus One?; Final remarks.; Main References; Additional References; Algebraic Geometry over Q; 1. Faisceaux arithmetiques coherents.; 1-1 Heights.; 1-2 Basic theorems of algebraic number theory; 1-3 The paper of Arakelov; 1-4 Cohomology of coherent sheaves; 1-5 More applications of Corollary 1 1-6 The degree of a sub variety is the self-intersection.1-7 Grothendieck-Riemann-Roch?; 2. A la recherche de petits points: Numerical properties of the relative dualizing.; 2-1 wX/Ok is big (i.e. points are not too small).; 2-2 When is (wX/Ok.wX/Ok) > 0?; 2-3 wX/Ok must be small; 2-4 The instrinsic small points conjecture.; 3. What is our subject?; 3-1 Integral models or adelic studies; 3-2 What metrics to choose; 3-3 Galois action Summary This book contains seven lectures delivered at The Maurice Auslander Memorial Conference at Brandeis University in March 1995. The variety of topics covered at the conference reflects the breadth of Maurice Auslander's contribution to mathematics, which includes commutative algebra and algebraic geometry, homological algebra and representation theory. He was one of the founding fathers of homological ring theory and representation theory of Artin algebras. Undoubtedly, the most characteristic feature of his mathematics was the profound use of homological and functorial techniques. For any researcher into representation theory, algebraic or arithmetic geometry, this book will be a valuable resource Notes "Transferred to digital printing 2002." Title from PDF title page (viewed on Apr. 9, 2013) "Lectures delivered at the Maurice Auslander Memorial Conference at Brandeis University in March 1995"--Page 4 of cover "Conference was held ... March 24-26, 1995"--Preface Bibliography Includes bibliographical references Subject Representations of algebras -- Congresses Geometry, Algebraic -- Congresses Commutative algebra -- Congresses Representations of algebras -- Congresses Geometry, Algebraic -- Congresses Commutative algebra -- Congresses MATHEMATICS -- Group Theory. Commutative algebra Geometry, Algebraic Representations of algebras Algebraische Geometrie Darstellungstheorie Algebra Kommutative Algebra Dimension n Algebraïsche meetkunde. Representatie (wiskunde) Géométrie algébrique -- Congrès. Représentations d'algèbres -- Congrès. Algèbres commutatives -- Congrès. Genre/Form Conference papers and proceedings Form Electronic book Author Martsinkovsky, A. (Alex) Todorov, G. (Gordana) Auslander, Maurice Maurice Auslander Memorial Conference (1995 : Brandeis University) ISBN 9781107362482 1107362482

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