Foundations of arithmetic differential geometry / Alexandru Buium.

"The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the pr...

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Bibliographic Details
Main Author: Buium, Alexandru, 1955- (Author)
Format: Book
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2017]
Series:Mathematical surveys and monographs ; no. 222.
Subjects:
Table of Contents:
  • Introduction
  • Algebraic background
  • Classical differential geometry revisited
  • Arithmetic differential geometry : generalities
  • Arithmetic differential geometry : the case of GLn
  • Curvature and Galois groups of Ehresmann connections
  • Curvature of Chern connections
  • Curvature of Levi-Cività connections
  • Curvature of Lax connections
  • Open problems.