There is a theory of Grothendieck duality developed for Deligne–Mumford stacks, however in some applications it is desirable to consider morphisms between stacks that are not Deligne–Mumford. I will talk about an adaptation to ∞-categories of the formal story of Neeman's Grothendieck duality for tensor triangulated categories, and then explain how to use these categorical results to obtain geometric statements. I will apply this result to determinantal line bundles on moduli of sheaves on stacky curves. Namely, I will explain how these line bundles depend on the determinant of the vector bundle defining them, and point out where Grothendieck duality is needed.
This talk will be followed by the talk at University of Sydney on Friday February 28th, 12pm–1pm, where I will focus on the construction of moduli of sheaves on stacky curves, which is joint work with Chiara Damiolini, Vicky Hoskins and Lisanne Taams.