Authors:

Jonathan Pakianathan,  University of Rochester.

Sarah Witherspoon,  Ahmerst College.

Stephen Siegel (Appendix),  U. Mass., Amherst. 

Status: Preprint

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-Broue correspondence on blocks. Our description 
leads in particular to a homeomorphism between the Hochschild variety of 
the principal block and the variety for the ordinary group cohomology.
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.