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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 \mathbb{F}_1-scheme X involves besides X_{\mathbb{PZ}}, a \C-algebra \mathcal{A}_X, and each cyclotomic point of X_{\mathbb{Z}} coming from X must assign ‘values’ to the elements of \mathcal{A}_X. His choice of \mathcal{A}_X for the multiplicative group \mathbb{G}_m is that of continuous functions on the unit circle in \CWe 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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