A Fitting Lemma for Z/2-graded modules

Details A Fitting Lemma for Z/2-graded modules A Fitting Lemma for Z/2-graded modules

2002-02-22

arxiv.org/abs/math/0202227v1

Mathematics

Algebraic Geometry

14 pages Plain TeX; uses diagrams.tex

Scientific paper

We study the annihilator of the cokernel of a map of free Z/2-graded modules over a Z/2-graded skew-commutative algebra in characteristic 0 and define analogues of its Fitting ideals. We show that in the ``generic'' case the annihilator is given by a Fitting ideal, and explain relations between the Fitting ideal and the annihilator that hold in general. Our results generalize the classical Fitting Lemma, and extend the key result of Green [1999]. They depend on the Berele-Regev theory of representations of general linear Lie super-algebras.

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