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Original Articles

An Elementary Proof of Grothendieck's Nonvanishing Theorem

Pages 2994-2996 | Received 25 Oct 2007, Published online: 22 Sep 2009
 

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:

2000 Mathematics Subject Classification:

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.

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