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The ring of reciprocal polynomials and rank varieties
Author(s) -
Woodcock Chris
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp038
Subject(s) - mathematics , subvariety , variety (cybernetics) , algebraically closed field , rank (graph theory) , prime (order theory) , quotient , pure mathematics , commutative ring , reciprocal , algebra over a field , field (mathematics) , ring (chemistry) , combinatorics , commutative property , linguistics , statistics , philosophy , chemistry , organic chemistry
Let p be a prime and let G be a finite p ‐group. In a recent paper we introduced a commutative graded ℤ‐algebra R G (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 W G ( M ) is constructed quite explicitly as a determinantal subvariety of the variety of K ‐valued points of the spectrum of R G . Further, it is shown that the quotient variety W G ( M )/ G is inseparably isogenous to the usual cohomological support variety V G ( M ).