Algebraic Geometry
Part I: Schemes. With Examples and Exercises
Autoren: Görtz, Ulrich, Wedhorn, Torsten
Vorschau- Der Wegbegleiter in das Feld der modernen algebraischen Geometrie im Bachelor/Master Studium
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- Über dieses Lehrbuch
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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 - Über die Autor*innen
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Prof. Dr. Ulrich Görtz, Institut für Experimentelle Mathematik, Universität Duisburg-Essen.Essen.
Prof. Dr. Torsten Wedhorn, Institut für Mathematik, Universität Paderborn.
Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen.
Prof. Dr. Torsten Wedhorn, Department of Mathematics, University of Paderborn.
- Inhaltsverzeichnis (17 Kapitel)
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Introduction
Seiten 1-6
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Prevarieties
Seiten 7-39
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Spectrum of a Ring
Seiten 40-65
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Schemes
Seiten 66-92
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Fiber products
Seiten 93-117
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Inhaltsverzeichnis (17 Kapitel)
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Bibliografische Information
- Bibliographic Information
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- Buchtitel
- Algebraic Geometry
- Buchuntertitel
- Part I: Schemes. With Examples and Exercises
- Autoren
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- Ulrich Görtz
- Torsten Wedhorn
- Titel der Buchreihe
- Advanced Lectures in Mathematics
- Copyright
- 2010
- Verlag
- Vieweg+Teubner Verlag
- Copyright Inhaber
- Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden
- eBook ISBN
- 978-3-8348-9722-0
- DOI
- 10.1007/978-3-8348-9722-0
- Buchreihen ISSN
- 0932-7134
- Auflage
- 1
- Seitenzahl
- IV, 615
- Themen
