Foundations of Arithmetic Differential Geometry is popular PDF and ePub book, written by Alexandru Buium in 2023-11-20, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Foundations of Arithmetic Differential Geometry can be Read Online from any device for your convenience.
Foundations of Arithmetic Differential Geometry Book PDF Summary
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 matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Detail Book of Foundations of Arithmetic Differential Geometry PDF
- Author : Alexandru Buium
- Release : 20 November 2023
- Publisher : American Mathematical Society
- ISBN : 9781470475772
- Genre : Mathematics
- Total Page : 357 pages
- Language : English
- PDF File Size : 20,9 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book Foundations of Arithmetic Differential Geometry by Alexandru Buium, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.
