Acyclicity of Schur complexes and torsion freeness of Schur modules
Document Type
Article
Publication Date
10-1-2019
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.
Publication Title
Journal of Algebra
First Page Number
133
Last Page Number
158
DOI
10.1016/j.jalgebra.2019.05.035
Recommended Citation
Allahverdi, Muberra and Tchernev, Alexandre, "Acyclicity of Schur complexes and torsion freeness of Schur modules" (2019). Kean Publications. 1319.
https://digitalcommons.kean.edu/keanpublications/1319
