A relation between noncommutative geometry and arithmetic (= number theory) has been explored much in the work of Alain Connes and his collaborators, especially Marcolli and Consani.

Some surveys include

- P. Almeida,
*Noncommutative geometry and arithmetics*, Russian Journal of Mathematical Physics**16**, No. 3, 2009, pp. 350–362, doi - Matilde Marcolli,
*Lectures on arithmetic noncommutative geometry*, math/0409520

There is also another line of thought in the work Manin-Marcolli on the relation of Arakelov geometry and noncommutative geometry. Arakelov’s geometry is of course, motivated by number theory.

Independetly, one should also notice that the noncommutative geometry over non-archimedean fields is relevant for homological mirror symmetry as explored in the works of Maxim Kontsevich and Yan Soibelman.

Created on July 24, 2011 at 15:19:23. See the history of this page for a list of all contributions to it.