It's well known that if E is a vector bundle with Chern roots $a_1,\ldots, a_r$, then the Chern roots of the $p$th exterior power of E consist of all sums of $k$ distinct $a_i$'s. I would like to say the same is true if E is just a torsion-free coherent sheaf on $P^n$. It seems non-obvious, though, maybe because an exterior power isn't generally an additive functor.

Presumably this is either false or also well known, but I can't find a reference.

finiteresolutions. – Mariano Suárez-Alvarez♦ Mar 31 '10 at 4:45