A Hochschild Cohomology Comparison Theorem for Prestacks

Brace Algebras and the Cohomology Comparison Theorem

The Gerstenhaber and Schack cohomology comparison theorem asserts that there is a cochain equivalence between the Hochschild complex of a certain algebra and the usual singular cochain complex of a space. We show that this comparison theorem preserves the brace algebra structures. This result gives a structural reason for the recent results establishing fine topological structures on the Hochsc...

Second Hochschild Cohomology of Convolution Algebras

On the Cohomology Comparison Theorem

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category and the relative derived category of modules over the algebra associated to the presheaf are studied. We obtain a generalization of the Special Cohomology Com...

Hochschild Cohomology for Complex Spaces and Noetherian Schemes

The classical HKR-theorem gives an isomorphism of the n-th Hochschild cohomology of a smooth algebra and the n-th exterior power of its module of Kähler differentials. Here we generalize it for simplicial, graded and anticommutative objects in “good pairs of categories”. We apply this generalization to complex spaces and noetherian schemes and deduce two decomposition theorems for their (relati...

The Bv Algebra on Hochschild Cohomology Induced by Infinity Inner Products

Abstract. We define a BV-structure on the Hochschild-cohomology of a unital, associative algebra A with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomolog...