The support of local cohomology modules

2015/09/04 by Katzman, Mordechai, Zhang, Wenliang · 2 citations
#13A35 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.01519

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^j_I(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∈ R).

Cited by

• Koszul cohomology and support of local cohomology modules of complete intersections
• Local cohomology modules with nonclosed support

Related

• Toward an efficient algorithm for deciding the vanishing of local cohomology modules in prime characteristic
• A formalism of F-modules for rings with complete local finite F-representation type
• Computing the support of local cohomology modules
• Local cohomology modules with nonclosed support
• Associated primes and cofiniteness of local cohomology modules