Local cohomology modules of a smooth ℤ -algebra have finitely many associated primes

2013/04/30 by Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik +2 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #math.AC #math.AG #msc:13A35 #msc:13D45 #msc:13F20 #msc:13N10 #msc:14B15

paper · pdf · doi:10.1007/s00222-013-0490-z

openalex publication_date 2013/11/25 · arxiv created 2013/12/19 · arxiv updated 2015/06/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

Let R be a commutative Noetherian ring that is a smooth \mathbb Z-algebra. For each ideal I of R and integer k, we prove that the local cohomology module H^k_I(R) has finitely many associated prime ideals. This settles a crucial outstanding case of a conjecture of Lyubeznik asserting this finiteness for local cohomology modules of all regular rings.

Citations

• Éléments de géométrie algébrique : IV. Étude locale des schémas et des morphismes de schémas, Quatrième partie

Cited by

• Bhargav Bhatt (mathematician) [wikipedia]