  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.
