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arXiv · 2508.10668

Corings, their dual rings and relative (co)Hochschild cohomology

Jonathan Lindell
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Abstract

We show for a coring which is finitely generated projective as a left module that the Cartier cohomology is isomorphic to the relative Hochschild cohomology of the right algebra. Furthermore, we show that this isomorphism lifts to the level of $B_{\infty}$-algebras of the chain complexes, by showing that the opposite $B_{\infty}$-algebra of the relative Hochschild cochains of the right algebra is isomorphic to the $B_{\infty}$-algebra of Cartier cochains. Lastly, we apply this to entwining structures where the coalgebra is finite-dimensional, to get a description of the equivariant cohomology of the entwining structure as the relative Hochschild cohomology of the twisted convolution algebra.

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Jonathan Lindell. 2025-08-14. Corings, their dual rings and relative (co)Hochschild cohomology. https://arxiv.org/abs/2508.10668

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