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Algebraic Geometry I: Schemes = With Examples and Exercises /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Algebraic Geometry I: Schemes/ by Ulrich Görtz, Torsten Wedhorn.
其他題名:	With Examples and Exercises /
作者:	Görtz, Ulrich.
其他作者:	Wedhorn, Torsten.
面頁冊數:	VII, 626 p. 15 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Algebraic Geometry. -
電子資源:	https://doi.org/10.1007/978-3-658-30733-2
ISBN:	9783658307332

Algebraic Geometry I: Schemes = With Examples and Exercises /
Görtz, Ulrich.

Algebraic Geometry I: SchemesWith Examples and Exercises /[electronic resource] :by Ulrich Görtz, Torsten Wedhorn. - 2nd ed. 2020. - VII, 626 p. 15 illus.online resource. - 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 Görtz, 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:

670184
Algebraic Geometry.

LC Class. No.: QA564-609

Dewey Class. No.: 516.35

Algebraic Geometry I: Schemes = With Examples and Exercises /
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