Algebraic Geometry I: Schemes : With Examples and Exercises / by Ulrich Görtz, Torsten Wedhorn.

Format:

Book

Author/Creator:

Görtz, Ulrich, 1973- author.

Wedhorn, Torsten, author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (SpringerNature-11649)

Springer studium mathematik. Master 2509-9310

Springer Studium Mathematik - Master, 2509-9310

Language:

English

Subjects (All):

Geometry, Algebraic.

Algebraic Geometry.

Local Subjects:

Algebraic Geometry.

Physical Description:

1 online resource (VII, 626 pages) : 15 illustrations.

Edition:

Second edition 2020.

Contained In:

Springer Nature eBook

Place of Publication:

Wiesbaden : Springer Fachmedien Wiesbaden : Imprint: Springer Spektrum, 2020.

System Details:

text file PDF

Summary:

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 started, 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. For the second edition, several mistakes and many smaller errors and misprints have been corrected. 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 About the Authors Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt.

Contents:

Introduction

1 Prevarieties

2 Spectrum of a Ring

3 Schemes

4 Fiber products

5 Schemes over fields

6 Local Properties of Schemes

7 Quasi-coherent modules

8 Representable Functors

9 Separated morphisms

10 Finiteness Conditions

11 Vector bundles

12 Affine and proper morphisms

13 Projective morphisms

14 Flat morphisms and dimension

15 One-dimensional schemes

16 Examples. .

Other Format:

Printed edition:

ISBN:

978-3-658-30733-2

9783658307332

Access Restriction:

Restricted for use by site license.