The paper you refer to by Gérard Laumon appears to be:
 
*Comparaison de caractéristiques d'Euler-Poincaré en cohomologie l-adique,* 
C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 3, 209–212. 

According to the MathSciNet Review of this paper (reference MR0610321 (82e:14030)) by William E. Lang:

> As a corollary, the author deduces that if $k$ is algebraically closed, and if $X$ is a separated scheme of finite type over $k$, then for all $E_\lambda$-sheaves $\mathcal{F}$ on $X$, $\chi(X,\mathcal{F})=\chi_c(X,\mathcal{F})$. This corollary had been previously proved by A. Grothendieck for curves in all characteristics [ibid., (SGA 5 X), pp. 372–406], and in all dimensions when the characteristic of $k$ is zero.