Acyclicity of Schur complexes and torsion freeness of Schur modules

Muberra Allahverdi,Alexandre Tchernev

doi:10.1016/j.jalgebra.2019.05.035

Acyclicity of Schur complexes and torsion freeness of Schur modules

Muberra Allahverdi, Alexandre Tchernev

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https://doi.org/10.1016/j.jalgebra.2019.05.035

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Journal: Journal of Algebra	Publication Date: Jun 21, 2019
License type: publisher-specific-oa

Affiliation: Kean University, University at Albany, State University of New York

#Noetherian Commutative Ring #En Route + Show 8 more

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Abstract

Let R be a Noetherian commutative ring and M a R-module with pdRM≤1 that has rank. Necessary and sufficient conditions were provided in [1] for an exterior power ∧kM to be torsion free. When M is an ideal of R similar necessary and sufficient conditions were provided in [2] for a symmetric power SkM to be torsion free. We extend these results to a broad class of Schur modules Lλ/μM. En route, for any map of finite free R modules ϕ:F→G we also study the general structure of the Schur complexes Lλ/μϕ, and provide necessary and sufficient conditions for the acyclicity of any given Lλ/μϕ by computing explicitly the radicals of the ideals of maximal minors of all its differentials.

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