The support of local cohomology modules

Abstract

We describe the support of $F$-finite $F$-modules over polynomial rings $R$ of prime characteristic. Our description yields an algorithm to compute the support of such modules; the complexity of our algorithm is also analyzed. To the best of our knowledge, this is the first algorithm to avoid extensive use of Gröbner bases and hence of substantial practical value. We also use the idea behind this algorithm to prove that the support of $H_I^j(S)$ is Zariski closed for each ideal $I$ of $S$ where $R$ is noetherian commutative ring of prime characteristic with finitely many isolated singular points and $S=R/gR$ ($g\in R$).

To appear in International Mathematics Research Notices

References in corpus (1)

• On the upper semi-continuity of HSL numbers