Ebook: Foundations of arithmetic differential geometry
Author: Buium Alexandru
- Genre: Mathematics // Geometry and Topology
- Tags: Geometry Differential., MATHEMATICS -- Geometry -- General., Number theory -- Forms and linear algebraic groups -- Classical groups., Number theory -- Discontinuous groups and automorphic forms -- $p$-adic theory local fields., Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Local ground fields., Differential geometry -- Global differential geometry -- Methods of Riemannian geometry including PDE methods, curvature restrictions.
- Series: AMS Mathematical Surveys and Monographs 222
- Year: 2017
- Publisher: American Mathematical Society
- Language: English
- pdf
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 prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients Read more...
Abstract:
Introduces and develops an arithmetic analogue of classical differential geometry. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study Read more...
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