Acyclicity of Schur complexes and torsion freeness of Schur modules
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  for an exterior power ∧kM to be torsion free. When M is an ideal of R similar necessary and sufficient conditions were provided in  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.
Journal of Algebra
First Page Number
Last Page Number
Allahverdi, Muberra and Tchernev, Alexandre, "Acyclicity of Schur complexes and torsion freeness of Schur modules" (2019). Kean Publications. 1319.