Acyclicity of Schur complexes and torsion freeness of Schur modules
Journal of Algebra, ISSN: 0021-8693, Vol: 535, Page: 133-158
2019
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Article Description
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.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0021869319303308; http://dx.doi.org/10.1016/j.jalgebra.2019.05.035; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85068463636&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0021869319303308; https://digitalcommons.kean.edu/keanpublications/1319; https://digitalcommons.kean.edu/cgi/viewcontent.cgi?article=2318&context=keanpublications; https://dx.doi.org/10.1016/j.jalgebra.2019.05.035
Elsevier BV
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