A Property Of Local Cohomology Modules Of Polynomial Rings

Details A Property Of Local Cohomology Modules Of Polynomial Rings A Property Of Local Cohomology Modules Of Polynomial Rings

2010-01-19

arxiv.org/abs/1001.3363v1

Mathematics

Commutative Algebra

Scientific paper

Let $R=k[x_1,..., x_n]$ be a polynomial ring over a field $k$ of
characteristic $p>0,$ and let $I=(f_1,...,f_s)$ be an ideal of $R.$ We prove
that every associated prime $P$ of $H^i_I(R)$ satisfies $\text{dim}R/P\geqslant
n-\sum\text{deg}f_i.$ In characteristic 0 the question is open.

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