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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Quillen stratification for Hochschild cohomology of blocks

Authors: Jonathan Pakianathan and Sarah Witherspoon; and with an appendix by Stephen F. Siegel
Journal: Trans. Amer. Math. Soc. 358 (2006), 2897-2916
MSC (2000): Primary 20J06
Published electronically: December 20, 2005
MathSciNet review: 2216251
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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-Broué 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.

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Additional Information

Jonathan Pakianathan
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627

Sarah Witherspoon
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843

Stephen F. Siegel
Affiliation: Department of Computer Science, University of Massachusetts, Amherst, Massachusetts 01003-9264

Received by editor(s): March 3, 2004
Published electronically: December 20, 2005
Additional Notes: The second author was supported by National Security Agency Grant #MDS904-01-1-0067 and National Science Foundation Grant #DMS0245560.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.