Hochschild and block cohomology varieties are isomorphic

Autores: Markus Linckelmann
Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 2, 2010, págs. 389-411
Idioma: inglés
DOI: 10.1112/jlms/jdp078
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Resumen
- 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.