Ravi Vakil: The Rising Sea
The Rising Sea
Buch
- Foundations of Algebraic Geometry
Erscheint bald
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- Princeton University Press, 12/2025
- Einband: Kartoniert / Broschiert
- Sprache: Englisch
- ISBN-13: 9780691268675
- Umfang: 632 Seiten
- Erscheinungstermin: 16.12.2025
Achtung: Artikel ist nicht in deutscher Sprache!
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Klappentext
An accessible, motivated introduction to one of the most dynamic areas of mathematicsDecades ago, Mumford wrote that algebraic geometry ';seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics.' The revolution has now fully come to pass and has fundamentally changed how we think about many fields of mathematics. This book provides a thorough foundation in the powerful ideas that now shape the landscape, with an informal yet rigorous exposition that builds intuition for the formidable machinery. It begins with a discussion of categorical thinking and sheaves and then develops the notion of schemes and varieties as examples of ';geometric spaces' before discussing their specific aspects. The book goes on to cover topics such as dimension and smoothness, vector bundles and their natural generalizations, and important cohomological tools and their applications. Important optional topics are included in starred sections.
A comprehensive introduction certain to become the standard book on the subject
Features a wealth of exercises that enable students to learn by doing
Requires few prerequisites, developing the tools students need to succeed, from category theory and sheaf theory to commutative and homological algebra
Uses an example-driven approach that builds mathematical intuition
A self-contained textbook for graduate students and an essential reference for researchers