149 research outputs found
On injective resolutions of local cohomology modules
Let be a field of characteristic zero and let .
Let be an ideal in and let be the -local
cohomology module of with respect to .
Let . We prove that if is a prime ideal in with
Bass number then is a maximal ideal in
A short note on the non-negativity of partial Euler characteristics
Let be a Noetherian local ring, a finite -module
and x_1,...,x_n\in \m such that \lambda (M/\x M) is finite. Serre proved
that all partial Euler characteristics of with respect to \x is
non-negative. This fact is easy to show when contains a field. We give an
elementary proof of Serre's result when does not contain a field.Comment: 2 page
- …