An elementary proof of Grothendieck's Non-vanishing Theorem

Abstract

We give an elementary proof of Grothendieck's non-vanishing Theorem: For a finitely generated non-zero module $M$ over a Noetherian local ring $A$ with maximal ideal $\m$, the local cohomology module $H^{\dim M}_{\m}(M)$ is non-zero.

Title & abstract changed, some minor changes in the main body of the paper, 3 pages, To appear in Communications in Algebra