  We propose a slightly modified definition for the Fourier-Mukai transform (on
abelian varieties) that makes it much easier to remember various formulas. As
an application, we give relatively short proofs for two important theorems: the
characterization of GV-sheaves in terms of vanishing, due to Hacon; and fact
that M-regularity implies (continuous) global generation, due to Pareschi and
Popa.
