Covariant Functors and Asymptotic Stability
Tony Se · 2015 · arXiv
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Abstract (excerpt)
Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then the sets of associated primes of F(M/I^n M) and F(I^n-1 M / I^n M) and the J-depths of F(M/I^n M) and F(I^n-1 M / I^n M) become independent of n for large n. Next, we consider several examples in which F is a rather familiar functor, but is not coherent or not even finitely generated in general. In these cases, the set of associated primes of F(M/I^n M) still
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Metadata source: arXiv