A remark on the Fourier-Mukai transform (Q1902214)

The paper includes a generalization of the set-up for the Fourier-Mukai transform for a quadratic module over \(\mathbb{Z}\). The motivation lies in Mukai's claim that \(\text{SL}_2 (\mathbb{Z})\) acts on the derived category \(D^b (A)\) of coherent sheaves on an abelian variety \(A\) endowed with a principal symmetric polarization modulo shifts.