Algebraic Geometry: Schemes. with Examples and Exercises Part I

Algebraic Geometry: Schemes. with Examples and Exercises Part I

Paperback Advanced Lectures in Mathematics

By (author) Ulrich Görtz, By (author) Torsten Wedhorn

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  • Publisher: Vieweg+Teubner Verlag
  • Format: Paperback | 615 pages
  • Dimensions: 168mm x 240mm x 34mm | 1,161g
  • Publication date: 25 June 2010
  • Publication City/Country: Weisbaden
  • ISBN 10: 3834806765
  • ISBN 13: 9783834806765
  • Edition statement: 2010 ed.
  • Illustrations note: biography
  • Sales rank: 555,760

Product description

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.

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Author information

Prof. Dr. Ulrich Gortz, Institut fur Experimentelle Mathematik, Universitat Duisburg-Essen.Essen. Prof. Dr. Torsten Wedhorn, Institut fur Mathematik, Universitat Paderborn. Prof. Dr. Ulrich Gortz, Institute of Experimental Mathematics, University Duisburg-Essen. Prof. Dr. Torsten Wedhorn, Department of Mathematics, University of Paderborn.

Back cover copy

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 Gortz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, University of Paderborn"

Table of contents

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