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Algebraic Geometry II: Cohomology of Schemes With Examples and Exercises - Couverture souple

Livre 4 sur 4: Springer Studium Mathematik - Master

Görtz, Ulrich; Wedhorn, Torsten

 
9783658430306: Algebraic Geometry II: Cohomology of Schemes With Examples and Exercises
Couverture souple
ISBN 10 : 3658430303 ISBN 13 : 9783658430306
Editeur : Springer Spektrum, 2023

Synopsis

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 étale morphisms including the étale 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

Prof. Dr. Ulrich Görtz, Department of Mathematics, University of Duisburg-Essen

Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer Spektrum
Date d'édition
2023
Langue
anglais
ISBN 10 
3658430303
ISBN 13 
9783658430306
Reliure
Broché
Numéro d'édition
1
Nombre de pages
876
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