### Oct 31, 2008

#### Halloween-talk : prep-notes

Posted by lievenlb in KapranovSmirnov, Kurokawa2005, Manin1995, Manin2006, Manin2008, news • No commentsThe prep-notes for the halloween-talk on “F_un and other ghost stories” at the Arts are available.

The prep-notes for the halloween-talk on “F_un and other ghost stories” at the Arts are available.

Handwritten notes from the third and fourth lectures at the MPI F_un seminar.

Katia Consani gave a talk “On the notion of geometry over F_un” at the Fields institute.

Last time, we tried to generalize the Connes-Consani approach to the noncommutative world but didn’t specify what we meant by noncommutative varieties or schemes and how they were related to Grothendieck’s dessins d’enfants. That’s what we will do today.

“One can postulate, of course, that spec(F_un) is the absolute point, but the real problem is to develop non-trivial consequences of this point of view.”

Handwritten notes from the lectures at the MPI F_un seminar

In a follow-up post, F_un and the braid group – a note of skepticism, arguments are collected **against** the claim that the d-string braid group should be invertible dxd matrices over the polynomials over F_un.

It is perhaps surprising that Alain Connes and Katia Consani, two icons of noncommutative geometry, restrict themselves to define **commutative** algebraic geometry over the field with one element. Remains the fact that their approach screams for a noncommutative extension.

Don’t be fooled by introductory remarks to the effect that ‘the field with one element was conceived by Jacques Tits…’ Let’s have it out into the open : F_un mathematics’ goal is no less than proving the Riemann Hypothesis.

Grothendieck’s anabelian geometry is an example of noncommutative F_un geometry. Javier starts this series with ramblings on how the folklore about F_un can be used to relate linear and permutation representations of finite groups.