September 2008 Archives

Sep 22, 2008

F_un and braid groups

Posted by in KapranovSmirnov, undergraduate 2 comments

We have seen before that the symmetric group S(n) has a F-un interpretation as the linear group GL(n) over the field with one element. Hence, we can ask whether there is also a F-un interpretation of the n-string braid group and of the above group-morphism.

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.

Sep 22, 2008

Looking for F_un

Posted by in Connes-C-M-2008, featured, Soule1999, Soule2004, undergraduate 1 comment

In recent years several people spend a lot of energy looking for properties of an elusive object : the field with one element or in French : “F-un”. One of the motivations is the hope to prove the Riemann hypothesis by mimicking Weil’s proof in the case of curves.

Sep 21, 2008


Posted by in library, Manin2008 No comments

Yuri I. Manin : Cyclotomy and analytic geometry over F_un, arXived on September 9th, 2008 arXiv:0809.1564v1

Sep 21, 2008


Posted by in Connes-Consani2008, library No comments

Alain Connes and Caterina Consani : On the notion of geometry over F_un, arXived on September 17th,200b as arXiv:0809.2926

Sep 21, 2008


Posted by in Connes-C-M-2008, library No comments

Alain Connes, Caterina Consani and Matilde Marcolli : Fun with F_un, arXived on June 14th, 2000 as arXiv:0806.2401

Sep 21, 2008


Posted by in Durov2007, library No comments

Nikolai Durov : New Approach to Arakelov Geometry, arXived April 16th, 2007 arXiv:0704.2030v1

Sep 21, 2008


Posted by in library, Manin2006 No comments

Yuri I. Manin : The notion of dimension in geometry and algebra, Bull. AMS 43 (2006) 139-161.

Sep 21, 2008


Posted by in Deitmar2006b, library No comments

Anton Deitmar : F_un schemes and toric varieties, arXived on August 7th,2006 as arXiv:math.NT/0608179