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

Un crit\`ere d'\'epointage des sections $l$-adiques