We show that dualising transfer maps in Hochschild cohomology of symmetric algebras over complete discrete valuations rings commutes with Tate duality. This is analogous to a similar result for Tate cohomology of symmetric algebras over fields. We interpret both results in the broader context of Calabi-Yau triangulated categories.
Vanishing of self-extensions over symmetric algebras
Derived equivalence classification of symmetric algebras of domestic type
A multiplicity one theorem for $\mathrm{GL}_n$ and $\mathrm{SL}_n$ over complete discrete valuation rings
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