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Arithmetic Differential Equations
 
Alexandru Buium University of New Mexico, Albuquerque, NM
Arithmetic Differential Equations
Hardcover ISBN:  978-0-8218-3862-4
Product Code:  SURV/118
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1345-3
Product Code:  SURV/118.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-3862-4
eBook: ISBN:  978-1-4704-1345-3
Product Code:  SURV/118.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Arithmetic Differential Equations
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Arithmetic Differential Equations
Alexandru Buium University of New Mexico, Albuquerque, NM
Hardcover ISBN:  978-0-8218-3862-4
Product Code:  SURV/118
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1345-3
Product Code:  SURV/118.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-3862-4
eBook ISBN:  978-1-4704-1345-3
Product Code:  SURV/118.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1182005; 310 pp
    MSC: Primary 14; 30; Secondary 53; 37;

    This monograph contains exciting original mathematics that will inspire new directions of research in algebraic geometry. Developed here is an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operator is replaced by a "Fermat quotient operator", and differential equations (viewed as functions on jet spaces) are replaced by "arithmetic differential equations". The main application of this theory concerns the construction and study of quotients of algebraic curves by correspondences with infinite orbits. Any such quotient reduces to a point in algebraic geometry. But many of the above quotients cease to be trivial (and become quite interesting) if one enlarges algebraic geometry by using arithmetic differential equations in place of algebraic equations.

    This book, in part, follows a series of papers written by the author. However, a substantial amount of the material has never been published before. For most of the book, the only prerequisites are the basic facts of algebraic geometry and algebraic number theory. It is suitable for graduate students and researchers interested in algebraic geometry and number theory.

    Readership

    Graduate students and research mathematicians interested in algebraic geometry and number theory.

  • Table of Contents
     
     
    • Chapters
    • 1. Preliminaries from algebraic geometry
    • 2. Outline of $\delta $–geometry
    • 3. Global theory
    • 4. Local theory
    • 5. Birational theory
    • 6. Spherical correspondences
    • 7. Flat correspondences
    • 8. Hyperbolic correspondences
  • Additional Material
     
     
  • Reviews
     
     
    • The book is written very clearly and organized beautifully.

      Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1182005; 310 pp
MSC: Primary 14; 30; Secondary 53; 37;

This monograph contains exciting original mathematics that will inspire new directions of research in algebraic geometry. Developed here is an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operator is replaced by a "Fermat quotient operator", and differential equations (viewed as functions on jet spaces) are replaced by "arithmetic differential equations". The main application of this theory concerns the construction and study of quotients of algebraic curves by correspondences with infinite orbits. Any such quotient reduces to a point in algebraic geometry. But many of the above quotients cease to be trivial (and become quite interesting) if one enlarges algebraic geometry by using arithmetic differential equations in place of algebraic equations.

This book, in part, follows a series of papers written by the author. However, a substantial amount of the material has never been published before. For most of the book, the only prerequisites are the basic facts of algebraic geometry and algebraic number theory. It is suitable for graduate students and researchers interested in algebraic geometry and number theory.

Readership

Graduate students and research mathematicians interested in algebraic geometry and number theory.

  • Chapters
  • 1. Preliminaries from algebraic geometry
  • 2. Outline of $\delta $–geometry
  • 3. Global theory
  • 4. Local theory
  • 5. Birational theory
  • 6. Spherical correspondences
  • 7. Flat correspondences
  • 8. Hyperbolic correspondences
  • The book is written very clearly and organized beautifully.

    Mathematical Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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