Hochschild and block cohomology varieties are isomorphic

Markus Linckelmann

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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 (‘Hochschild cohomology and Linckelmann cohomology for blocks of finite groups’, J. Pure Appl. Algebra 178 (2003) 87–100; ‘Quillen stratification for Hochschild cohomology of blocks’, Trans. Amer. Math. Soc. 358 (2005) 2897–2916). 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.
Original languageEnglish
Pages (from-to)389-411
Number of pages25
JournalJournal of the London Mathematical Society
Issue number2
Early online date12 Feb 2010
Publication statusPublished - Apr 2010


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