un dessin d’enfancePosted by lievenlb on Dec 1, 2008 in Manin2008, news • 1 comment
Last week I gave a talk at the 60th birthday conference for Jacques Alev. If you are interested in the slides, here they are. The official title was supposed to be “dessins d’enfants” with this summary
I will try to convince you that Grothendieck’s ‘dessins d’enfant’ form an example of a noncommutative manifold over the mythical field with one element (in the sense of Soule and Connes-Consani).
However, dessins only appear at the final slide. The main part of the talk consisted in explaining one sentence in Manin’s recent paper (page 4, line 3):
Soule’s definition of an -scheme involves besides , a -algebra , and each cyclotomic point of coming from must assign ‘values’ to the elements of . His choice of for the multiplicative group is that of continuous functions on the unit circle in … We suggest to consider the ring of Habiro’s analytic functions…
I promised Jacques to do a proper write-up of the talk (and include some more details on the final slide) so I might as well do a couple of posts on it, later.Print This Post