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Representation theory and algebraic geometry /
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 algebrai...
| Clasificación: | Libro Electrónico |
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| Autor Corporativo: | |
| Otros Autores: | , , |
| Formato: | Electrónico Congresos, conferencias eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
1997.
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| Colección: | London Mathematical Society lecture note series ;
238. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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