A note on injectivity of Frobenius on local cohomology of global complete intersections

作者：Canton Eric^*

来源：Journal of Pure and Applied Algebra, 2016, 220(8): 2879-2885.

DOI：10.1016/j.jpaa.2016.01.006

Given a graded complete intersection ideal J = (f(1),..., f(c)) subset of k[x(0),..., x(n)] = S, where k is a field of characteristic p > 0 such that [k : k(p)] < infinity, we show that if S/J has an isolated non-F-pure point then the Frobenius action on top local cohomology H-m(n+1-c)(S/J) is injective in sufficiently negative degrees, and we compute the least degree of any kernel element. If S/J has an isolated singularity, we are also able to give an effective bound on p ensuring the Frobenius action on H-m(n+1-c)(S/J) is injective in all negative degrees, extending a result of Bhatt and Singh in the hypersurface case.

• 出版日期2016-8