Axiomization of passage from "local" structure to "global" object
Author(s)
Bibliographic Information
Axiomization of passage from "local" structure to "global" object
（Memoirs of the American Mathematical Society, no. 485）
American Mathematical Society, 1993
Available at 19 libraries
Note
Includes bibliographical references (p. 107)
"January 1993, volume 101, number 485 (end of volume)" -- T.p
Description and Table of Contents
Description
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.
Table of Contents
Terminology Canopies Canopies and colimits Smoothing Local and global structures.
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