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Kevin H. Lin
Kevin H. Lin
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The HKR theorem for cohomology in characteristic zero says that if $R$ is a regular, commutative $k$ algebra ($char(k) = 0$) then a certain map $\bigwedge^* Der(R) \to CH^*(R,R)$ (where $\wedge^* Der(R)$ has zero defferentialdifferential)is is a quasi-isomorphism and moreoverof dg vector spaces, that is, it induces an isomorphimisomorphism of algebrasgraded vector spaces on the cohomology.

Can the HKR morphism be extended to an $A_\infty$ morphism? IsIs there a refinement in this spirit to make up for the fact that it is not, on the nose, a morphism of dg-algebras?

The HKR theorem for cohomology in characteristic zero says that if $R$ is a regular, commutative $k$ algebra ($char(k) = 0$) then a certain map $\bigwedge^* Der(R) \to CH^*(R,R)$ (where $\wedge^* Der(R)$ has zero defferential)is a quasi-isomorphism and moreover induces an isomorphim of algebras on the cohomology.

Can the HKR morphism be extended to an $A_\infty$ morphism? Is there a refinement in this spirit to make up for the fact that it is not, on the nose, a morphism of dg-algebras?

The HKR theorem for cohomology in characteristic zero says that if $R$ is a regular, commutative $k$ algebra ($char(k) = 0$) then a certain map $\bigwedge^* Der(R) \to CH^*(R,R)$ (where $\wedge^* Der(R)$ has zero differential) is a quasi-isomorphism of dg vector spaces, that is, it induces an isomorphism of graded vector spaces on cohomology.

Can the HKR morphism be extended to an $A_\infty$ morphism? Is there a refinement in this spirit to make up for the fact that it is not, on the nose, a morphism of dg-algebras?

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Ian Shipman
Ian Shipman
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Is there a refinement of the Hochschild-Kostant-Rosenberg theorem for cohomology?

The HKR theorem for cohomology in characteristic zero says that if $R$ is a regular, commutative $k$ algebra ($char(k) = 0$) then a certain map $\bigwedge^* Der(R) \to CH^*(R,R)$ (where $\wedge^* Der(R)$ has zero defferential)is a quasi-isomorphism and moreover induces an isomorphim of algebras on the cohomology.

Can the HKR morphism be extended to an $A_\infty$ morphism? Is there a refinement in this spirit to make up for the fact that it is not, on the nose, a morphism of dg-algebras?