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”.)

This is part 1 of a series of two lectures which I recently gave at a seminar in Ghent (April 28, 2011): “Introduction to Absolute Arithmetic”.

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.

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.

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.