Derived categories of equivariant coherent sheaves (A07)

• Subject Area: Mathematics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 286237555

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
• Subproject of: TRR 195: Symbolic Tools in Mathematics and their Application
• Applicant Institution: Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau
• Project Heads: Professor Dr. Mohamed Barakat; Professor Dr. Frank-Olaf Schreyer