Cart
Free US shipping over $10
Proud to be B-Corp

Algebraic Geometry II: Cohomology of Schemes Ulrich Goertz

Algebraic Geometry II: Cohomology of Schemes By Ulrich Goertz

Algebraic Geometry II: Cohomology of Schemes by Ulrich Goertz


Summary

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 etale morphisms including the etale fundamental group.

Faster Shipping

Get this product faster from our US warehouse

Algebraic Geometry II: Cohomology of Schemes Summary

Algebraic Geometry II: Cohomology of Schemes: With Examples and Exercises by Ulrich Goertz

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 etale morphisms including the etale 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.

About Ulrich Goertz

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

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

Table of Contents

Introduction.- 17 Differentials.- 18 Etale and smooth morphisms.- 19 Local complete intersections.- 20 The etale 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.

Additional information

CIN3658430303G
9783658430306
3658430303
Algebraic Geometry II: Cohomology of Schemes: With Examples and Exercises by Ulrich Goertz
Used - Good
Paperback
Springer Fachmedien Wiesbaden
2023-12-08
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us

Customer Reviews - Algebraic Geometry II: Cohomology of Schemes