A Kleiman-Bertini Theorem for sheaf tensor products

Details A Kleiman-Bertini Theorem for sheaf tensor products A Kleiman-Bertini Theorem for sheaf tensor products

2006-01-10

arxiv.org/abs/math/0601202v4

Mathematics

Algebraic Geometry

5 pages; v2: corrected misspelled title; v3: smoothness of group G added to hypotheses, additional remarks on page 1, slight e

Scientific paper

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.

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