An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Axiomization of Passage from ‘Local’ Structure to ‘Global’ Object

Available Formats:
Electronic ISBN: 978-1-4704-0062-0
Product Code: MEMO/101/485.E
List Price: $31.00 MAA Member Price:$27.90
AMS Member Price: $18.60 Click above image for expanded view Axiomization of Passage from ‘Local’ Structure to ‘Global’ Object Available Formats:  Electronic ISBN: 978-1-4704-0062-0 Product Code: MEMO/101/485.E  List Price:$31.00 MAA Member Price: $27.90 AMS Member Price:$18.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1011993; 107 pp
MSC: Primary 14; 18;

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.

Graduate students studying schemes for the first time; algebraic geometers with interest in foundational issues.

• Chapters
• Introduction
• Part I. Terminology
• Part II. Canopies
• Part III. Canopies and colimits
• Part IV. Smoothing
• Part V. Local and global structures
• Request Review Copy
• Get Permissions
Volume: 1011993; 107 pp
MSC: Primary 14; 18;

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.