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.
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.
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.
At the Max-Planck Institute for Mathematics in Bonn a weekly study seminar on F_un will start tuesday october 7th at 14.00 hrs.
Alain Connes explaining the paper “Fun with F_un” on YouTube!
To Gavin Wraiht a mathematical phantom is a “nonexistent entity which ought to be there but apparently is not; but nevertheless obtrudes its effects so convincingly that one is forced to concede a broader notion of existence”. Mathematics’ history is filled with phantoms getting the kiss of life.
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.
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.
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.
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.