Abstract
For a flat commutative -algebra such that the enveloping algebra is noetherian, given a finitely generated bimodule , we show that the adic completion of the Hochschild cohomology module is naturally isomorphic to . To show this, we make a detailed study of derived completion as a functor over a nonnoetherian ring , prove a flat base change result for weakly proregular ideals, and prove that Hochschild cohomology and analytic Hochschild cohomology of complete noetherian local rings are isomorphic, answering a question of Buchweitz and Flenner. Our results make it possible for the first time to compute the Hochschild cohomology of over any noetherian ring , and open the door for a theory of Hochschild cohomology over formal schemes.
Citation
Liran Shaul. "Hochschild cohomology commutes with adic completion." Algebra Number Theory 10 (5) 1001 - 1029, 2016. https://doi.org/10.2140/ant.2016.10.1001
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