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Asymptotic Associate Primes. (arXiv:1709.06253v2 [math.AC] UPDATED)
来源于:arXiv
We investigate three cases regarding asymptotic associate primes. First,
assume $ (A,\mathfrak{m}) $ is an excellent Cohen-Macaulay (CM) non-regular
local ring, and $ M = \operatorname{Syz}^A_1(L) $ for some maximal CM $ A
$-module $ L $ which is free on the punctured spectrum. Let $ I $ be a normal
ideal. In this case, we examine when $ \mathfrak{m} \notin
\operatorname{Ass}(M/I^nM) $ for all $ n \gg 0 $. We give sufficient evidence
to show that this occurs rarely. Next, assume that $ (A,\mathfrak{m}) $ is
excellent Gorenstein non-regular isolated singularity, and $ M $ is a CM $ A
$-module with $\operatorname{projdim}_A(M) = \infty $ and $ \dim(M) = \dim(A)
-1 $. Let $ I $ be a normal ideal with analytic spread $ l(I) < \dim(A) $. In
this case, we investigate when $\mathfrak{m} \notin \operatorname{Ass}
\operatorname{Tor}^A_1(M, A/I^n)$ for all $n \gg 0$. We give sufficient
evidence to show that this also occurs rarely. Finally, suppose $ A $ is a
local complete intersection ring. 查看全文>>