Let $X$ be an algebraic variety over $\mathbb C$ and let $\mathcal F$ be a constructible sheaf on $X$. It is well-known that the Euler characteristic of the cohomology of $\mathcal F$ is equal to the Euler characteristic of cohomology with compact support. What is the right reference for this result? 
In $l$-adic cohomology this was proved first by Laumon (I think) but over $\mathbb C$ this should have been known before.



Euler characteristic - reference question
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) by William E. Lang:



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> "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."
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According to the reference, that was in 1965–1966.


