Primes associated to multigraded modules

Let be a Noetherian multigraded ring, and let M be a finitely generated multigraded R-module. We investigate the asymptotic behavior of AssR0(Mn). In case R is generated in total degree one, we show that the expected stability occurs. We also consider several non-standard cases. For general -graded R, we show that {AssR0(Mn)} is eventually periodic, but need not be stable. For rings graded by , with t 2, we show that in some cases a form of periodicity holds, while in others there is a “cone” of stability.