Algebraic geometry and commutative algebra / Siegfried Bosch

By:

Bosch, Siegfried, 1944- [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Universitext | Springer eBook CollectionPublisher: London : Springer, [2022]Edition: Second editionDescription: 1 Online-Ressource (X, 504 Seiten) : IllustrationenISBN:

9781447175230

Subject(s):

Additional physical formats: 9781447175223 | Erscheint auch als: 9781447175223 Druck-Ausgabe | Erscheint auch als: 9781447175247 Druck-Ausgabe | Erscheint auch als: Algebraic geometry and commutative algebra. Druck-Ausgabe Second edition. London : Springer, 2022. X, 504 SeitenRVK: RVK: SK 240DOI: DOI: 10.1007/978-1-4471-7523-0Online resources:

Summary: 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.Summary: 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.PPN: PPN: 1800273010Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

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