The Geometry of Schemes (Graduate Texts in Mathematics, 197)

Eisenbud, David

ISBN 10: 0387986375 / ISBN 13: 9780387986371

Editore: Springer, 2000

Fairly worn, but readable and intact. If applicable: Dust jacket, disc or access code may not be included. Codice articolo 3IIT7G005OJU_ns

Riassunto:

The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his coworkers. It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. It integrates algebraic number theory with algebraic geometry, fulfilling the dreams of earlier generations of number theorists. This integration has led to proofs of some of the major conjectures in number theory (Deligne's proof of the Weil Conjectures, Faltings proof of the Mordell Conjecture). This book is intended to bridge the chasm between a first course in classical algebraic geometry and a technical treatise on schemes. It focuses on examples, and strives to show "what is going on" behind the definitions. There are many exercises to test and extend the reader's understanding. The prerequisites are modest: a little commutative algebra and an acquaintance with algebraic varieties, roughly at the level of a one-semester course. The book aims to show schemes in relation to other geometric ideas, such as the theory of manifolds. Some familiarity with these ideas is helpful, though not required.

Recensione: "A great subject and expert authors!"
Nieuw Archief voor Wiskunde,June 2001

"Both Eisenbud and Harris are experienced and compelling educators of modern mathematics. This book is strongly recommended to anyone who would like to know what schemes are all about."
Newsletter of the New Zealand Mathematical Society, No. 82, August 2001

Dati bibliografici

Titolo: The Geometry of Schemes (Graduate Texts in ...
Casa editrice: Springer
Data di pubblicazione: 2000
Legatura: Brossura
Condizione: Acceptable