Let R0β be any domain, let R=R0β[U1β,...,Usβ]/I, where U1β,...,Usβ are indeterminates of some positive degrees, and IβR0β[U1β,...,Usβ] is a homogeneous ideal. The main theorem in this paper is states that all the associated primes of H:=HR+βsβ(R) contain a certain non-zero ideal c(I) of R0β called the
``content'' of I. It follows that the support of H is simply V(\content(I)R + R_+) (Corollary 1.8) and, in particular, H vanishes if and only if c(I) is the unit ideal. These results raise the question of whether local cohomology modules have finitely many minimal associated primes-- this paper provides further evidence in favour of such a result. Finally, we give a very short proof of a weak version of the monomial conjecture based on these results
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.