A kleiman-bertini theorem for sheaf tensor products

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Ezra, M; Speyer, DE

Published Date

  • January 1, 2008

Published In

Volume / Issue

  • 17 / 2

Start / End Page

  • 335 - 340

International Standard Serial Number (ISSN)

  • 1056-3911

Digital Object Identifier (DOI)

  • 10.1090/s1056-3911-07-00479-1

Citation Source

  • Scopus