Quillen stratification for hochschild cohomology of blocks Academic Article uri icon


  • We decompose the maximal ideal spectrum of the Hochschild cohomology ring of a block of a finite group into a disjoint union of subvarieties corresponding to elementary abelian p-subgroups of a defect group. These subvarieties are described in terms of group cohomological varieties and the Alperin-Brou correspondence on blocks. Our description leads in particular to a homeomorphism between the Hochschild variety of the principal block and the group cohomological variety. The proofs require a result of Stephen F. Siegel, given in the Appendix, which states that nilpotency in Hochschild cohomology is detected on elementary abelian p-subgroups. 2005 American Mathematical Society.

published proceedings

  • Transactions of the American Mathematical Society

author list (cited authors)

  • Pakianathan, J., Witherspoon, S., & Siegel, S. F.

complete list of authors

  • Pakianathan, J||Witherspoon, S||Siegel, SF

publication date

  • July 2006