  Fix a variety X with a transitive (left) action by an algebraic group G. Let
E and F be coherent sheaves on X. We prove that, for elements g in a dense open
subset of G, the sheaf Tor_i^X(E, g F) vanishes for all i > 0. When E and F are
structure sheaves of smooth subschemes of X in characteristic zero, this
follows from the Kleiman-Bertini theorem; our result has no smoothness
hypotheses on the supports of E or F, or hypotheses on the characteristic of
the ground field.
