Un critère d'épointage des sections $l$-adiques

The cuspidalization conjecture emerged as an approach of Grothendieck's famous section conjecture. We address a weak form of it by using a mild generalization of a theorem of Uwe Jannsen which describes exactly when the $l$-adic homology of an open curve is a pure Galois representation. We also give some concrete examples of modular curves for which the cuspidalization is possible at the $l$-adic level.

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