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Let $k$ be a field of characteristic $p > 0$ such that $[k:k^p] < \infty$ andlet $f \in R = k[x_0, ..., x_n]$ be homogeneous of degree $d$. We obtain asharp bound on the degrees in which the Frobenius action on$H^n_\mathfrak{m}(R/fR)$ can be injective when $R/fR$ has an isolatednon-F-pure point at $\mathfrak{m}$. As a corollary, we show that if$(R/fR)_\mathfrak{m}$ is not F-pure then $R/fR$ has an isolated non-F-purepoint at $\mathfrak{m}$ if and only if the Frobenius action is injective indegrees $\le -n(d-1)$.

A Note on Injectivity of Frobenius on Local Cohomology of Hypersurfaces