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Axiomization of Passage from "Local" Structure to "Global" Object (Memoirs of the American Mathematical Society)
Rok: 1993
ISBN: 9780821825464
OKCZID: 110344125
Citace (dle ČSN ISO 690):
FEIT, Paul. Axiomization of passage from "local" structure to "global" object. Providence, R.I.: American Mathematical Society, 1993. 107 s. Memoirs of the American Mathematical Society, 485.
Anotace
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.