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Axiomization of Passage from ‘Local’ Structure to ‘Global’ Object
 
Front Cover for 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
Front Cover for Axiomization of Passage from `Local' Structure to `Global' Object
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  • Front Cover for Axiomization of Passage from `Local' Structure to `Global' Object
  • Back Cover for Axiomization of Passage from `Local' Structure to `Global' Object
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.

    Readership

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

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Part I. Terminology
    • Part II. Canopies
    • Part III. Canopies and colimits
    • Part IV. Smoothing
    • Part V. Local and global structures
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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.

Readership

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
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