Algebraic Geometry I: Schemes
With Examples and Exercises
(Sprache: Englisch)
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New Textbook on Algebraic Geometry
Klappentext zu „Algebraic Geometry I: Schemes “
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.
Inhaltsverzeichnis zu „Algebraic Geometry I: Schemes “
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.
Autoren-Porträt von Ulrich Görtz, Torsten Wedhorn
Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-EssenProf. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt
Bibliographische Angaben
- Autoren: Ulrich Görtz , Torsten Wedhorn
- 2020, 2. Aufl., VII, 626 Seiten, Masse: 16,9 x 24,1 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3658307323
- ISBN-13: 9783658307325
Sprache:
Englisch
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