Acyclicity of Schur complexes and torsion freeness of Schur modules
Autor: | Muberra Allahverdi, Alexandre B. Tchernev |
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Rok vydání: | 2019 |
Předmět: | |
Zdroj: | Journal of Algebra. 535:133-158 |
ISSN: | 0021-8693 |
DOI: | 10.1016/j.jalgebra.2019.05.035 |
Popis: | Let R be a Noetherian commutative ring and M a R-module with pd R M ≤ 1 that has rank. Necessary and sufficient conditions were provided in [1] for an exterior power ∧ k M to be torsion free. When M is an ideal of R similar necessary and sufficient conditions were provided in [2] for a symmetric power S k M to be torsion free. We extend these results to a broad class of Schur modules L λ / μ M . En route, for any map of finite free R modules ϕ : F → G we also study the general structure of the Schur complexes L λ / μ ϕ , and provide necessary and sufficient conditions for the acyclicity of any given L λ / μ ϕ by computing explicitly the radicals of the ideals of maximal minors of all its differentials. |
Databáze: | OpenAIRE |
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