Algebraic Geometry II: Cohomology of Schemes (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
869
Utgivningsdatum
2023-11-23
Upplaga
1st ed. 2023
Förlag
Springer Spektrum
Illustrationer
153 Illustrations, black and white; VII, 869 p. 153 illus.
Dimensioner
244 x 170 x 44 mm
Vikt
1376 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9783658430306

Algebraic Geometry II: Cohomology of Schemes

With Examples and Exercises

av Ulrich Grtz, Torsten Wedhorn
Häftad,  Engelska, 2023-11-23
1145
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This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and tale morphisms including the tale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.
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Övrig information

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

Innehållsförteckning

Introduction.- 17 Differentials.- 18 tale and smooth morphisms.- 19 Local complete intersections.- 20 The tale topology.- 21 Cohomology of sheaves of modules.- 22 Cohomology of quasi-coherent modules.- 23 Cohomology of projective and proper schemes.- 24 Theorem on formal functions.- 25 Duality.- 26 Curves.- 27 Abelian schemes.- F Homological algebra.- G Commutative algebra II.

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