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Algebraic geometry. = with examples ...

Wedhorn, Torsten.

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Algebraic geometry. = with examples and exercises /. I,. Schemes

Record Type:	Electronic resources : Monograph/item
Title/Author:	Algebraic geometry./ by Ulrich Gortz, Torsten Wedhorn.
Reminder of title:	with examples and exercises /
remainder title:	Schemes
Author:	Gortz, Ulrich.
other author:	Wedhorn, Torsten.
Published:	Wiesbaden :Springer Fachmedien Wiesbaden : : 2020.,
Description:	vii, 626 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Geometry, Algebraic. -
Online resource:	https://doi.org/10.1007/978-3-658-30733-2
ISBN:	9783658307332

Algebraic geometry. = with examples and exercises /. I,. Schemes
Gortz, Ulrich.

Algebraic geometry.with examples and exercises /I,Schemes[electronic resource] :Schemesby Ulrich Gortz, Torsten Wedhorn. - Second edition. - Wiesbaden :Springer Fachmedien Wiesbaden :2020. - vii, 626 p. :ill., digital ;24 cm. - Springer studium mathematik - master,2509-9310. - Springer studium mathematik - master..

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.

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 Gortz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt.

ISBN: 9783658307332

Standard No.: 10.1007/978-3-658-30733-2doiSubjects--Topical Terms:

532048
Geometry, Algebraic.

LC Class. No.: QA564 / .G67 2020

Dewey Class. No.: 516.35

Algebraic geometry. = with examples and exercises /. I,. Schemes
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245 1 0 $a Algebraic geometry. $n I, $p Schemes $h [electronic resource] : $b with examples and exercises / $c by Ulrich Gortz, Torsten Wedhorn.
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300 $a vii, 626 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer studium mathematik - master, $x 2509-9310
505 0 $a 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.
520 $a 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 Gortz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt.
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