An elementary proof of Grothendieck's Non-vanishing Theorem

2007/10/31 by Tony J. Puthenpurakal, Puthenpurakal, Tony J.
Computer Science · Mathematics · #13A30 (Secondary) #13D45 #14B15 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13A30 #msc:13D45 #msc:14B15

paper · pdf · doi:10.48550/arxiv.0710.5863

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

openalex publication_date 2007/10/31 · arxiv created 2008/06/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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