Associate primes, grades, and finite lengths of F(M/I_1^{n_1}...I_r^{n_r}N) are eventually stable or polynomial, with a sharp degree bound.
Asymptotic linear bounds of Castelnuovo-Mumford regularity in multigraded modules
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Coherent functors, powers of ideals, and asymptotic stability
Associate primes, grades, and finite lengths of F(M/I_1^{n_1}...I_r^{n_r}N) are eventually stable or polynomial, with a sharp degree bound.