The Rising Sea: Foundations of Algebraic Geometry

Vakil, Ravi

ISBN 10: 0691268673 / ISBN 13: 9780691268675

Editore: Princeton University Press, 2025

Codice articolo 18403826232

Riassunto:

An accessible, motivated introduction to one of the most dynamic areas of mathematics

Decades 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 understanding 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.

• Provides a comprehensive introduction certain to become the standard 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
• Is a self-contained textbook for graduate students and an essential reference for researchers

Dati bibliografici

Titolo: The Rising Sea: Foundations of Algebraic ...
Casa editrice: Princeton University Press
Data di pubblicazione: 2025
Legatura: Brossura
Condizione: New