Resumen de Hochschild and block cohomology varieties are isomorphic

Markus Linckelmann

• 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.