Pham Hung Quy
Reputation
1,472
Next privilege 2,000 Rep.
 14h awarded Revival 17h awarded Revival 1d 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 20 answered invariants that can be measured by Local Cohomology Jan 11 answered Ring with Cohen-Macaulay canonical module Dec 29 answered Maximal Cohen-Macaulay modules of type one Dec 11 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 11 answered The finiteness of the associated primes of $Ext^i_R(R/I, M)$ Sep 18 awarded Yearling Sep 7 awarded Nice Question 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 1 revised Is an irreducible ideal in $R$ also irreducible in $R[x]$? added 105 characters in body Sep 1 revised Is an irreducible ideal in $R$ also irreducible in $R[x]$? added 180 characters in body Sep 1 answered Graded-irreducible ideals are irreducible? Aug 31 awarded Custodian Aug 31 reviewed Approve Is an irreducible ideal in $R$ also irreducible in $R[x]$? Aug 31 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 $R[x]$? added 695 characters in body Aug 28 revised Is an irreducible ideal in $R$ also irreducible in $R[x]$? added 9 characters in body Aug 28 answered Is an irreducible ideal in $R$ also irreducible in $R[x]$?