Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero

Collas, Benjamin

doi:10.5802/jtnb.813

Cited by 3 publications

(1 citation statement)

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“…The main result of the present article follows [Col12b,Col12a,CM14] and provides an answer to these questions in the case of cyclic stack inertias I x, see Theorem 4.8: Theorem (A). For any cyclic stack inertia group I = <γ> of M g, [m] , there exists a geometric Galois representation ρ s which induces a Gal(Q/Q)-action on I given by χ-conjugacy, i.e.…”

Section: Introductionmentioning

confidence: 83%

On Galois action on stack inertia of moduli spaces of curves

Collas,

Maugeais

2014

Preprint

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We establish that the geometric action of the absolute Galois group Gal( Q/Q) on the étale fundamental group of moduli spaces of curves induces a Galois action on its stack inertia subgroups, and that this action is given by cyclotomy conjugacy. This result extends the special case of inertia without étale factorisation previously established by the authors. It is here obtained in the general case by comparing deformations of Galois actions.Since the cyclic stack inertia corresponds to the first level of the stack stratification of the space, this results, by analogy with the arithmetic of the Deligne-Mumford stratification, opens the way to a systematic Galois study of the stack inertia through the corresponding stratification of the moduli stack.

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Section: Introductionmentioning

confidence: 83%