the Fourier transform sends complexes of sheaves on the total space of E to complexes of sheaves on the total space of the dual bundle E*
I only accepted Manjul Bhargava's solution because Mumford's proof of the GFGA theorem appeared in his answer to the problem set by me.
V. Kac, Infinite Dimensional Lie Algebras, Birkhäuser, Boston, 1983
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