Co-𝑡-structures on derived categories of coherent sheaves and the cohomology of tilting modules

Abstract

We construct a co- t t -structure on the derived category of coherent sheaves on the nilpotent cone N \mathcal {N} of a reductive group, as well as on the derived category of coherent sheaves on any parabolic Springer resolution. These structures are employed to show that the push-forwards of the “exotic parity objects” (considered by Achar, Hardesty, and Riche [Transform. Groups 24 (2019), pp. 597–657]), along the (classical) Springer resolution, give indecomposable objects inside the coheart of the co- t t -structure on N \mathcal {N} . We also demonstrate how the various parabolic co- t t -structures can be related by introducing an analogue to the usual translation functors. As an application, we give a proof of a scheme-theoretic formulation of the relative Humphreys conjecture on support varieties of tilting modules in type A A for p > h p>h .