Transactions of the American Mathematical Society

Author(s): Jonathan Pakianathan; Sarah Witherspoon; and with an appendix by Stephen F. Siegel
Journal: Trans. Amer. Math. Soc. 358 (2006), 2897-2916.
MSC (2000): Primary 20J06
Posted: December 20, 2005
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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

-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

-subgroups.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20J06

Jonathan Pakianathan
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: jonpak@math.rochester.edu

Sarah Witherspoon
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: sjw@math.tamu.edu

Stephen F. Siegel
Affiliation: Department of Computer Science, University of Massachusetts, Amherst, Massachusetts 01003-9264
Email: siegel@cs.umass.edu

DOI: 10.1090/S0002-9947-05-04012-2
PII: S 0002-9947(05)04012-2
Received by editor(s): March 3, 2004
Posted: 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.
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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