Absolute Arithmetic at the 6th European Congress of Mathematics !
The mini-symposium “Absolute Arithmetic and -Geometry” is part of the official scientific programme of the prestigious quadrennial European Congress of Mathematics (July 2-7 2012, Krakow, Poland). This conference is widely considered to be one of the most important mathematical gatherings around. The general character of the programme provides attendees with a unique chance of an [...]
Scheme theory over the field of characteristic one
Second part in a series which I gave at a seminar in Ghent (April 28, 2011): “Scheme theory over the field of characteristic one”. (The first part being “Introduction to Absolute Arithmetic”.)
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.
Absolute Arithmetic at the 6th European Congress of Mathematics !
The mini-symposium “Absolute Arithmetic and -Geometry” is part of the official scientific programme of the prestigious quadrennial European Congress of Mathematics (July 2-7 2012, Krakow, Poland). This conference is widely considered to be one of the most important mathematical gatherings around. The general character of the programme provides attendees with a unique chance of an [...]
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.
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.”