Introduces filtrations in chiral homology, linking it to Poisson homology in smooth elliptic curves, proposing implications for finite dimensionality.
We introduce filtrations in chiral homology complexes of smooth elliptic curves, exploiting the mixed Hodge structure on cohomology groups of configuration spaces. We use these to relate the chiral homology of a smooth elliptic curve with coefficients in a vertex algebra with the Poisson homology of the associated Poisson scheme. As an application we deduce finite dimensionality results for chiral homology in low degrees.
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Ekeren et al. (2026) studied this question.
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