The Rising Sea (eBook)

Foundations of Algebraic Geometry

Ravi Vakil (Autor)

eBook Download: PDF

2025
689 Seiten
Princeton University Press (Verlag)
978-0-691-26868-2 (ISBN)

Infos

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 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 subjectFeatures a wealth of exercises that enable students to learn by doingRequires few prerequisites, developing the tools students need to succeed, from category theory and sheaf theory to commutative and homological algebraUses an example-driven approach that builds mathematical intuitionIs a self-contained textbook for graduate students and an essential reference for researchers

Produkt-Details

• Erscheint lt. Verlag: 21.10.2025
• Zusatzinfo: 100 b/w illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: affine schemes • algebraic closure • Algebraic Geometry • Algebraic Varieties • artinian rings • Berkovich Spaces • categorical thinking • category theory • Characteristic Classes • chow rings • Cohen-Macaulay rings • coherent sheaves • cohomological tools • commutative algebra. • Commutative algebra • complete local rings • completions • complex geometry • Dedekind domains • depth • Differential Geometry • Dimension Theory • discrete valuation rings • étale cohomology • factorial rings • field extensions • formal schemes • functors • Galois Theory • geometric spaces • Gorenstein rings • graduate mathematics • Grothendieck Topology • Height • henselian rings • Higher Mathematics • hirzebruch-riemann-roch • Homological algebra • ideals • Intersection theory • Krull dimension • Localization • Maximal ideals • modules • Morphisms • natural transformations • Noetherian rings • normal rings • Number Theory • Prime ideals • principal ideal domains • Projective varieties • quasi-coherent sheaves • regular local rings • regular rings • Riemann-Roch theorem • rigid analytic geometry • Rings • schemes • scheme theory • Serre Duality • sheaf theory • Sheaves • Smoothness • spectrum • transcendence degree • tropical geometry • valuation rings • Varieties • Vector Bundles
• ISBN-10: 0-691-26868-1 / 0691268681
• ISBN-13: 978-0-691-26868-2 / 9780691268682