1.

Record Nr.

UNINA9910438150003321

Autore

Bosch Siegfried

Titolo

Algebraic Geometry and Commutative Algebra / / by Siegfried Bosch

Pubbl/distr/stampa

London : , : Springer London : , : Imprint : Springer, , 2013

ISBN

1-4471-4829-0

Edizione

[1st ed. 2013.]

Descrizione fisica

1 online resource (514 p.)

Collana

Universitext, , 0172-5939

Disciplina

516.35

Soggetti

Algebraic geometry

Commutative algebra

Commutative rings

Algebraic Geometry

Commutative Rings and Algebras

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents.



Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.