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# Documents  Hain, Richard | enregistrements trouvés : 2

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## Mixed motives associated to elliptic curves Hain, Richard | CIRM H

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Research talks;Algebraic and Complex Geometry

The absolute Galois group of the rational numbers acts on the various flavours (profinite, prounipotent, pro-$\ell$) of the fundamental group of a smooth projective curve over the rationals. The image of the corresponding homomorphism normalizes the image of the profinite mapping class group in the automorphism group of the geometric fundamental group of the curve. The image of the Galois action modulo these “geometric automorphisms” is independent of the curve. A basic problem is to determine this image. This talk is a report on a joint project with Francis Brown whose goal is to understand the image mod geometric automorphisms in the prounipotent case. Standard arguments reduce the problem to one in genus 1, where one can approach the problem by studying the periods of iterated integrals of modular forms and their relation to multiple zeta values. The absolute Galois group of the rational numbers acts on the various flavours (profinite, prounipotent, pro-$\ell$) of the fundamental group of a smooth projective curve over the rationals. The image of the corresponding homomorphism normalizes the image of the profinite mapping class group in the automorphism group of the geometric fundamental group of the curve. The image of the Galois action modulo these “geometric automorphisms” is ...

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## Moduli spaces of Riemann surfaces Farb, Benson ; Hain, Richard ; Looijenga, Eduard | American Mathematical Society;Institute for Advanced Study 2013

Ouvrage

- x; 356 p.
ISBN 978-0-8218-9887-1

IAS/Park City mathematics series , 0020

Localisation : Collection 1er étage

théorie des modules # surfaces de Riemann # théorie de Teichmüller

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