Axiomization of Passage from `Local' Structure to `Global' Object

Download or read book Axiomization of Passage from `Local' Structure to `Global' Object written by Paul Feit and published by American Mathematical Soc.. This book was released on 1993 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.