Oct 9, 2008

Gadgets a la Soulé

Posted by in graduate, Soule2004 3 comments

Inspired by the equivalent definition of a scheme as a particular kind of functor, Soulé gives his definition of a gadget over F_un as a couple consisting on a functor, that takes the rôle of the functor of points, and an algebra, which encodes a ‘topology at infinity’ and gives us the extra information that is missing in the functor.

Oct 4, 2008

The skeleton of Soulé’s F_un geometry

Posted by in featured, graduate, Soule2004 No comments

Any possible definition of a variey over F_un should have a nice extension of scalars to the integers. In particular, we might expect to be able to control the behavior of such extension for the easiest family of rings defined over F_un: its finite abelian extensions F_un^n.

Sep 22, 2008

F_un linear algebra

Posted by in graduate, KapranovSmirnov No comments

Over F_un vectorspaces are pointed sets. One can also do linear algebra over the F_un extension fields F_un^n. Vectorspaces are then pointed sets having a free action of n-th roots of unity.

Sep 22, 2008

The F_un folklore

Posted by in graduate, KapranovSmirnov, Manin1995 1 comment

The followers of F-un have their own collection of semi-secret texts, surrounded by whispers, of which they try to decode every single line in search of enlightenment. Fortunately, you do not have to search the shelves of the Bibliotheque National in Paris, but the depths of the internet to find them as huge, bandwidth-unfriendly, scanned documents.