Algebraic Geometry I

Schemes With Examples and Exercises

  • Ulrich Görtz
  • Torsten Wedhorn

Table of contents

  1. Front Matter
    Pages I-VII
  2. Ulrich Görtz, Torsten Wedhorn
    Pages 1-6
  3. Ulrich Görtz, Torsten Wedhorn
    Pages 7-39
  4. Ulrich Görtz, Torsten Wedhorn
    Pages 40-65
  5. Ulrich Görtz, Torsten Wedhorn
    Pages 66-92
  6. Ulrich Görtz, Torsten Wedhorn
    Pages 93-117
  7. Ulrich Görtz, Torsten Wedhorn
    Pages 118-144
  8. Ulrich Görtz, Torsten Wedhorn
    Pages 145-168
  9. Ulrich Görtz, Torsten Wedhorn
    Pages 169-204
  10. Ulrich Görtz, Torsten Wedhorn
    Pages 205-225
  11. Ulrich Görtz, Torsten Wedhorn
    Pages 226-240
  12. Ulrich Görtz, Torsten Wedhorn
    Pages 241-285
  13. Ulrich Görtz, Torsten Wedhorn
    Pages 286-319
  14. Ulrich Görtz, Torsten Wedhorn
    Pages 320-365
  15. Ulrich Görtz, Torsten Wedhorn
    Pages 366-422
  16. Ulrich Görtz, Torsten Wedhorn
    Pages 423-484
  17. Ulrich Görtz, Torsten Wedhorn
    Pages 485-502
  18. Ulrich Görtz, Torsten Wedhorn
    Pages 503-540
  19. Back Matter
    Pages 541-615

About this book

Introduction

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

Keywords

Algebraic Geometry Geometry Schemes Vector bundles algebra morphisms

Authors and affiliations

  • Ulrich Görtz
    • 1
  • Torsten Wedhorn
    • 2
  1. 1.Institute of Experimental MathematicsUniversity Duisburg-EssenEssenGermany
  2. 2.University of PaderbornDepartment of MathematicsPaderbornGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-8348-9722-0
  • Copyright Information Vieweg+Teubner Verlag | GWV Fachverlage GmbH, Wiesbaden 2010
  • Publisher Name Vieweg+Teubner
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-8348-0676-5
  • Online ISBN 978-3-8348-9722-0
  • About this book