Many interesting varieties arise as a quotient orbifold [X/G] of a variety X by an action of a finite group G. We are interested in the situation where there exists a resolution r:Y -> X/G inducing an exact equivalence of derived categories D^b (Y) -> D_G^b (X) - D^b ([X/G]), where D_G^b (X) := D^b (Coh_G X) is the bounded derived category of G-equivariant coherent sheaves on X. Any triangulated equivalence of those derived categories is necessarily a (generalised) Fourier-Mukai equivalence. One goal of this project is to render the above setup constructive when such resolutions Y are known to exist.
DFG Programme
CRC/Transregios
