Papers Published
Abstract:
Fix a variety X with a transitive (left) action by an algebraic group G. Let ε and ℱ be coherent sheaves on X. We prove that for elements g in a dense open subset of G, the sheaf Tor¡X- (ε, gℱ) vanishes for all i > 0. When ε 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 ε or ℱ, or hypotheses on the characteristic of the ground field.