Hochschild and block cohomology varieties are isomorphic

Linckelmann, M. (2010). Hochschild and block cohomology varieties are isomorphic. Journal of the London Mathematical Society, 81(2), pp. 389-411. doi: 10.1112/jlms/jdp078

Abstract

We show that the varieties of the Hochschild cohomology of a block algebra and its block cohomology are isomorphic, implying positive answers to questions of Pakianathan and Witherspoon in [16] and [17]. We obtain as a consequence that the cohomology H*(G; k) of a finite group G with coefficients in a field k of characteristic p is a quotient of the Hochschild cohomology of the principal block of kG by a nilpotent ideal.