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un dessin d’enfance

Posted By __lievenlb__ On December 1, 2008 @ 11:44 am In __Manin2008,news__ | __1 Comment__

Last week I gave a talk at the 60th birthday conference for Jacques Alev ^{[1]}. If you are interested in the slides, here they are ^{[2]}.
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 ^{[3]} (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.

Article printed from F_un mathematics: **http://cage.ugent.be/~kthas/Fun**

URL to article: **http://cage.ugent.be/~kthas/Fun/index.php/un-dessin-denfance.html**

URLs in this post:

[1] 60th birthday conference for Jacques Alev: **http://loic.foissy.free.fr/colloque/programme.html**

[2] here they are: **http://cage.ugent.be/~kthas/Fun/DATA/Alev60.pdf**

[3] Manin’s recent paper: **http://cage.ugent.be/~kthas/Fun/index.php/manin2008.html**

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