Algebraic Geometry I [recurso electrónico] : Schemes With Examples and Exercises / by Ulrich Görtz, Torsten Wedhorn.
Tipo de material: TextoEditor: Wiesbaden : Vieweg+Teubner, 2010Descripción: IV, 615 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783834897220Tema(s): Mathematics | Algebra | Mathematics | AlgebraFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 512 Clasificación LoC:QA150-272Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA150 -272 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 377098-2001 |
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QA150 -272 Algebraic Patching | QA150 -272 From Objects to Diagrams for Ranges of Functors | QA150 -272 Discrete Mathematics in Statistical Physics | QA150 -272 Algebraic Geometry I | QA150 -272 Álgebra Linear | QA150 -272 Structured Matrix Based Methods for Approximate Polynomial GCD | QA150 -272 Algorithms for Quadratic Matrix and Vector Equations |
Prevarieties -- Spectrum of a Ring -- Schemes -- Fiber products -- Schemes over fields -- Local Properties of Schemes -- Quasi-coherent modules -- Representable Functors -- Separated morphisms -- Finiteness Conditions -- Vector bundles -- Affine and proper morphisms -- Projective morphisms -- Flat morphisms and dimension -- One-dimensional schemes -- Examples.
This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes. Prevarieties - Spectrum of a Ring - Schemes - Fiber products - Schemes over fields - Local properties of schemes - Quasi-coherent modules - Representable functors - Separated morphisms - Finiteness Conditions - Vector bundles - Affine and proper morphisms - Projective morphisms - Flat morphisms and dimension - One-dimensional schemes - Examples Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, University of Paderborn
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