Algebraic Geometry I: Schemes (häftad)
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Format
Häftad (Paperback / softback)
Språk
Tyska
Antal sidor
626
Utgivningsdatum
2020-07-28
Upplaga
2nd corr. ed. 2020
Förlag
Springer Spektrum
Originalspråk
German
Medarbetare
Wedhorn, Torsten
Illustrationer
15 Illustrations, black and white; VII, 626 p. 15 illus.
Dimensioner
244 x 170 x 33 mm
Vikt
999 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9783658307325

Algebraic Geometry I: Schemes

With Examples and Exercises

av Ulrich Grtz, Torsten Wedhorn
Häftad,  Tyska, 2020-07-28
942
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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 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.
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Övrig information

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

Innehållsförteckning

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.

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