
I will explain basics of geometry in which commutative rings
are replaced by by structures without addition, and its relations with
Arakelov geometry. In this geometry, Spec Z has a non--trivial product with itself.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/2804