
Algebraic Geometry I: Schemes
With Examples and Exercises
Springer Spektrum (Publisher)
2nd Edition
Published on 28. July 2020
Book
Paperback/Softback
VII, 626 pages
978-3-658-30732-5 (ISBN)
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.
More details
Product info
Book
Series
Edition
2nd corr. ed. 2020
Language
English
Place of publication
Wiesbaden
Germany
Publishing group
Springer Fachmedien Wiesbaden GmbH
Product notice
Paperback (trade)
Unsewn / adhesive bound
Illustrations
15 s/w Abbildungen
Bibliography; 15 Illustrations, black and white
Dimensions
Height: 240 mm
Width: 168 mm
Thickness: 34 mm
Weight
1050 gr
ISBN-13
978-3-658-30732-5 (9783658307325)
DOI
10.1007/978-3-658-30733-2
Schweitzer Classification
Other editions
Additional editions

E-Book
07/2020
2nd Edition
Springer Spektrum
€85.59
Available for download
Previous edition

Book
06/2010
Vieweg+Teubner Verlag
€64.19
Article exhausted; check for reprint
Persons
Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen
Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt
Content
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.