Fitting's Lemma for -graded modules
Authors:
David Eisenbud and Jerzy Weyman
Journal:
Trans. Amer. Math. Soc. 355 (2003), 4451-4473
MSC (2000):
Primary 13C99, 13C05, 13D02, 16D70, 17B70
DOI:
https://doi.org/10.1090/S0002-9947-03-03198-2
Published electronically:
June 10, 2003
MathSciNet review:
1990758
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a map of free modules over a commutative ring
. Fitting's Lemma shows that the ``Fitting ideal,'' the ideal of
minors of
, annihilates the cokernel of
and is a good approximation to the whole annihilator in a certain sense. In characteristic 0 we define a Fitting ideal in the more general case of a map of graded free modules over a
-graded skew-commutative algebra and prove corresponding theorems about the annihilator; for example, the Fitting ideal and the annihilator of the cokernel are equal in the generic case. Our results generalize the classical Fitting Lemma in the commutative case and extend a key result of Green (1999) in the exterior algebra case. They depend on the Berele-Regev theory of representations of general linear Lie superalgebras. In the purely even and purely odd cases we also offer a standard basis approach to the module
when
is a generic matrix.
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Additional Information
David Eisenbud
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Email:
de@msri.org
Jerzy Weyman
Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email:
j.weyman@neu.edu
DOI:
https://doi.org/10.1090/S0002-9947-03-03198-2
Received by editor(s):
March 20, 2002
Received by editor(s) in revised form:
May 29, 2002
Published electronically:
June 10, 2003
Additional Notes:
The second named author is grateful to the Mathematical Sciences Research Institute for support in the period this work was completed. Both authors are grateful for the partial support of the National Science Foundation.
Article copyright:
© Copyright 2003
American Mathematical Society