Axiomization of Passage from `Local' Structure to `Global' Object (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Feit, Paul

Softcover

ISBN 10: 0821825461 ISBN 13: 9780821825464

Publisher: American Mathematical Society, 1993

Synopsis

Requiring only familiarity with the terminology of categories, this book will interest algebraic geometers and students studying schemes for the first time. Feit translates the geometric intuition of local structure into a purely categorical format, filling a gap at the foundations of algebraic geometry. The main result is that, given an initial category ${\mathcal C}$ of ""local"" objects and morphisms, there is a canonical enlargement of ${\mathcal C}$ to a category ${\mathcal C}^{gl}$ which contains all 'global' objects whose local structure derives from ${\mathcal C}$ and which is functorially equivalent to the traditional notion of 'global objects'. Using this approach, Feit unifies definitions for numerous technical objects of algebraic geometry, including schemes, Tate's rigid analytic spaces, and algebraic spaces.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1993
• Language: English
• ISBN 10: 0821825461
• ISBN 13: 9780821825464
• Binding: Paperback
• Number of pages: 107