Quillen stratification for hochschild cohomology of blocks

abstract

• 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.

authors

• Witherspoon, Sarah

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

published in

• Transactions of the American Mathematical Society  Journal

start page

• 2897

end page

• 2916

volume

• 358

issue

• 7