Homological duality for covering groups of reductive \(p\)-adic groups (Q2111349)

In the paper under the review, the authors extend the properties of the homological duality functor to the case of the Hecke algebra of a finite central extension of a reductive \(p\)-adic group. Although the paper is mostly expository, a new and self-contained proof of the main properties of the homological duality functor is obtained. Among other results, it is proven that it gives rise to the Schneider-Stuhler duality. The authors also study the Grothendieck-Serre duality with respect to the Bernstein center and show that on admissible modules this functor agrees with the contragradient duality. Certain conditions under which these three dualities coincide on finite length modules in a given block are provided.