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Bulletin of the London Mathematical Society Advance Access originally published online on May 7, 2009
Bulletin of the London Mathematical Society 2009 41(4):654-662; doi:10.1112/blms/bdp038
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© 2009 London Mathematical Society

The ring of reciprocal polynomials and rank varieties

Chris Woodcock

Institute of Mathematics, Statistics and Actuarial Science
University of Kent
Canterbury
CT2 7NF
United Kingdom

Received 20 May 2008. Revision received 13 January 2009.

Let p be a prime and let G be a finite p-group. In a recent paper we introduced a commutative graded Z-algebra RG (which classifies the so-called convolutions on G). Now let K be an algebraically closed field of characteristic p and let M be a non-zero finitely generated K[G]-module. A general rank variety WG(M) is constructed quite explicitly as a determinantal subvariety of the variety of K-valued points of the spectrum of RG. Further, it is shown that the quotient variety WG(M)/G is inseparably isogenous to the usual cohomological support variety VG(M).

2000 Mathematics Subject Classification 13A50, 20C05, 20C20, 20J06 (primary).


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