In treating both of these examples, as well as all the examples to come, we will use the Euler-Poincaré formula, cf. [**Ray**, Thm. 1] or [**Ka-GKM**, 2.3.1] or [**Ka-SE**, 4.6, (v) atop p. 113] or [**De-ST**, 3.2.1], to compute the “dimension” of the object *N* in question.

Let us briefly recall the general statement of the Euler-Poincaré formula, and then specialize to the case at hand. Let *X* be a projective, smooth, nonsingular curve over an algebraically closed field *k* in which *ℓ* is invertible, *U ⊂ X* a dense open set in *X*, and *V ⊂ U* a dense open set in *U*. Let *G* be a constructible Q_{ℓ}-sheaf on *U* which is lisse on *V* of rank *r* := *gen.rk.*(*G*). We view *G|V* as a representation of π_{1}(*V*). For each point ...

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