Algebraic Geometry and Commutative Algebra

2012. Buch. x, 504 S.: Bibliographien. Softcover
Springer ISBN 978-1-4471-4828-9
Format (B x L): 15,5 x 23,5 cm
Gewicht: 783 g
In englischer Sprache
Das Werk ist Teil der Reihe:
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, like algebraic number theory. 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. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite 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. This way 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.
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Explains schemes in algebraic geometry from a beginner's level up to advanced topics such as smoothness and ample invertible sheaves Is self-contained and well adapted for self-study Includes prerequisites from commutative algebra in a separate part Gives motivating introductions to the different themes, illustrated by typical examples Offers an abundance of exercises, specially adapted to the different sections