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comment invariants that can be measured by Local Cohomology
I mean the Faltings annihilator implies Theorem 1. By Faltings annihilator we have $\mathfrak{p} \in Var(\mathfrak{a})$ if and only if $$\mathrm{depth} R_{\mathfrak{p}} + \dim R/\mathfrak{p} < d.$$ The last one is equivalent to $\mathfrak{p} \in nCM(R)$.
Apr
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answered invariants that can be measured by Local Cohomology
Jan
11
answered Ring with Cohen-Macaulay canonical module
Dec
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answered Maximal Cohen-Macaulay modules of type one
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comment The finiteness of the associated primes of $Ext^i_R(R/I, M)$
the local condition is not important in this question. you can change $\mathbb{Z}[X]$ by $\mathbb{Q}[X,Y,Z]_{(X,Y,Z)}$ and the prime ideals $\{(p,X): p \text{ is prime}\}$ by $\{(X, Y+nZ) : n = 0, 1, ...\}$.
Dec
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answered The finiteness of the associated primes of $Ext^i_R(R/I, M)$
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Sep
4
comment Graded-irreducible ideals are irreducible?
Thank you Fred, I have a quick look their proof. They used the fact $I$ is irreducible iff the index of reducible of $I$ is one. So their proof need Noetheian condition. My proof is also true for $\mathbb{Z}$-graded (I fell it works for $\mathbb{N}^n$-graded also).
Sep
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revised Is an irreducible ideal in $R$ also irreducible in $R[x]$?
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Sep
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revised Is an irreducible ideal in $R$ also irreducible in $R[x]$?
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Sep
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answered Graded-irreducible ideals are irreducible?
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awarded  Custodian
Aug
31
reviewed Approve Is an irreducible ideal in $R$ also irreducible in $R[x]$?
Aug
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comment Is an irreducible ideal in $R$ also irreducible in $R[x]$?
I edited my answer more detail (add a Fact).
Aug
31
revised Is an irreducible ideal in $R$ also irreducible in $R[x]$?
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Aug
28
revised Is an irreducible ideal in $R$ also irreducible in $R[x]$?
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Aug
28
answered Is an irreducible ideal in $R$ also irreducible in $R[x]$?