Algebraic Geometry and Commutative Algebra

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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

Zusammenfassung

The present edition is a critical revision of the earlier text

Is self-contained and well adapted for self-study

Offers an abundance of exercises, specially adapted to the different sections

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2022
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Universitext
Inhalt:	X 504 S. 18 s/w Illustr. 504 p. 18 illus.
ISBN-13:	9781447175223
ISBN-10:	1447175220
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Bosch, Siegfried
Auflage:	2nd ed. 2022
Hersteller:	Springer London Springer-Verlag London Ltd. Universitext
Maße:	235 x 155 x 28 mm
Von/Mit:	Siegfried Bosch
Erscheinungsdatum:	23.04.2022
Gewicht:	0,774 kg

Artikel-ID: 121257298