outreach
Andre Weil on the Riemann hypothesis
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.
undergraduate
Connes-Consani for undergraduates (3)
Alain Connes and Katia Consani arXived the paper “On the notion of geometry over F_un” in which they refine and simplify Soule’s approach. This series tries to explain their construction to non-specialists in algebraic geometry.
graduate
Gadgets a la Soulé
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.
research
noncommutative F_un geometry (2)
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.
news
Anyone interested?
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 [...]
webcasts
Consani on F_un
Katia Consani gave a talk “On the notion of geometry over F_un” at the Fields institute.
quotes
Kapranov-Smirnov on F_un
“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.”
other blogs
Quomodocumque on F_un (Update 10-21)
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.