Hilbert functions of polynomial growth

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Let $R=k[x_1, dots , x_n]$. Let $M$ be a graded $R$-module whose hilbert function $h(i):=textdim_kM_i$ is well-defined and grows like a polynomial. Is $M$ a finitely generated $R$-module?




commutative-algebra




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    Take $M = R$ with trivial $R$ action.
    – anomaly
    Aug 2 at 1:16














up vote
1
down vote

favorite












Let $R=k[x_1, dots , x_n]$. Let $M$ be a graded $R$-module whose hilbert function $h(i):=textdim_kM_i$ is well-defined and grows like a polynomial. Is $M$ a finitely generated $R$-module?




commutative-algebra




share|cite|improve this question















  • 2




    Take $M = R$ with trivial $R$ action.
    – anomaly
    Aug 2 at 1:16












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Let $R=k[x_1, dots , x_n]$. Let $M$ be a graded $R$-module whose hilbert function $h(i):=textdim_kM_i$ is well-defined and grows like a polynomial. Is $M$ a finitely generated $R$-module?




commutative-algebra




share|cite|improve this question











Let $R=k[x_1, dots , x_n]$. Let $M$ be a graded $R$-module whose hilbert function $h(i):=textdim_kM_i$ is well-defined and grows like a polynomial. Is $M$ a finitely generated $R$-module?





commutative-algebra





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 2 at 0:57









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263




263







  • 2




    Take $M = R$ with trivial $R$ action.
    – anomaly
    Aug 2 at 1:16












  • 2




    Take $M = R$ with trivial $R$ action.
    – anomaly
    Aug 2 at 1:16







2




2




Take $M = R$ with trivial $R$ action.
– anomaly
Aug 2 at 1:16




Take $M = R$ with trivial $R$ action.
– anomaly
Aug 2 at 1:16















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