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Foundations of Arithmetic Differential Geometry

Title: Foundations of Arithmetic Differential Geometry | Author(s): Alexandru Buium | Publisher: American Mathematical Society | Year: 2017 | Language: English | Pages: 344 | Size: 4 MB | Extension: pdf 

Alexandru Buium: University of New Mexico, Albuquerque, NM

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 of integers with respect to the primes. The role of metrics is played by symmetric…

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