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

Achar, Pramod; Hardesty, William

doi:10.1090/ert/655

Co-$t$-structures on derived categories of coherent sheaves and the cohomology of tilting modules
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by Pramod N. Achar and William Hardesty;

Represent. Theory 28 (2024), 49-89

DOI: https://doi.org/10.1090/ert/655

Published electronically: February 2, 2024

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Abstract:

We construct a co-$t$-structure on the derived category of coherent sheaves on the nilpotent cone $\mathcal {N}$ 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-$t$-structure on $\mathcal {N}$. We also demonstrate how the various parabolic co-$t$-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 $A$ for $p>h$.

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