An Elementary Proof of Grothendieck's Nonvanishing Theorem

Abstract

We give an elementary proof of Grothendieck's nonvanishing Theorem: For a finitely generated nonzero module M over a Noetherian local ring A with maximal ideal 𝔪, the local cohomology module is nonzero.

Key Words:

• Local cohomology

2000 Mathematics Subject Classification:

• Primary 13D45
• Secondary 13C15

ACKNOWLEDGMENT

The author owes an intellectual debt to Prof. K. D. Joshi who taught him that it is sometimes easier to prove stronger results by induction. He also thanks the referee for many pertinent comments.

Notes

Communicated by A. Singh.

Dedicated to Prof. K. D. Joshi.