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Arithmetic Differential Equations
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Arithmetic Differential Equations

Arithmetic Differential Equations

Alexandru Buium - Collection Mathematical Surveys and Monographs

310 pages, parution le 27/10/2005

Résumé

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.

Sommaire

  • Main concepts and results
    • Preliminaries from algebraic geometry
    • Outline of $\delta$-geometry
  • General theory
    • Global theory
    • Local theory
    • Birational theory
  • Applications
    • Spherical correspondences
    • Flat correspondences
    • Hyperbolic correspondences
    • List of results
    • Bibliography
    • Index
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Caractéristiques techniques

  PAPIER
Éditeur(s) American Mathematical Society (AMS)
Auteur(s) Alexandru Buium
Collection Mathematical Surveys and Monographs
Parution 27/10/2005
Nb. de pages 310
Format 18 x 26
Couverture Relié
Poids 824g
Intérieur Noir et Blanc
EAN13 9780821838624
ISBN13 978-0-8218-3862-4

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