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bosch siegfried - algebraic geometry and commutative algebra

Algebraic Geometry and Commutative Algebra




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 04/2022
Edizione: 2nd ed. 2022





Trama

Algebraic Geometry is a fascinating branch of Mathematics that combines methods from both Algebra and Geometry. It transcends the limited scope of pure Algebra by means of geometric construction principles. Putting forward this idea, Grothendieck revolutionized Algebraic Geometry in the late 1950s by inventing schemes. Schemes now also play an important role in Algebraic Number Theory, a field that used to be far away from Geometry. The new point of view paved the way for spectacular progress, such as the proof of Fermat's Last Theorem by Wiles and Taylor.

This book explains the scheme-theoretic approach to Algebraic Geometry for non-experts, while more advanced readers can use it to broaden their view on the subject. A separate part presents the necessary prerequisites from Commutative Algebra, thereby providing an accessible and self-contained introduction to advanced Algebraic Geometry.

Every chapter of the book is preceded by a motivating introduction with an informal discussion of its contents and background. Typical examples, and an abundance of exercises illustrate each section. Therefore the book is an excellent companion for self-studying or for complementing skills that have already been acquired. It can just as well serve as a convenient source for (reading) course material and, in any case, as supplementary literature. The present edition is a critical revision of the earlier text.





Sommario

Rings and Modules.- The Theory of Noetherian Rings.- Integral Extensions.- Extension of Coefficients and Descent.- Homological Methods: Ext and Tor.- Affine Schemes and Basic Constructions.- Techniques of Global Schemes.- Etale and Smooth Morphisms.- Projective Schemes and Proper Morphisms.




Autore

Prof. Dr. Siegfried Bosch, Mathematical Institute, University of Münster, Münster, Germany











Altre Informazioni

ISBN:

9781447175223

Condizione: Nuovo
Collana: Universitext
Dimensioni: 235 x 155 mm Ø 783 gr
Formato: Brossura
Illustration Notes:X, 504 p. 18 illus.
Pagine Arabe: 504
Pagine Romane: x


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