I’m about to write a series of posts on Borger’s notion of geometry over the field with one element using lambda-rings. Problem remains : where should I post them? Here, or elsewhere? In other words, are there any humans left here (or are the 50 to 60 daily hits robot-performed), and, more importantly, are any [...]

Slides are available of a talk given last week in Reims on Manin’s analytic F_un-geometry.

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

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.”

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.

The Fields Institute organizes a Workshop on Arithmetic Geometry with talks by Soule, Consani and Durov a.o. and topics including Arakelov geometry (‘including the infinity-adic’) and ‘Generalized rings and schemes’.

Our highly paid IC-experts do not know that MPG also stand for the Max Planck Gesellschaft and that the string .mpg. is contained in all official email-addresses from MPI … This almost prematurely killed this blog.