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

• 成果类型: Article
• 署名作者: Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K.; Zhang, Wenliang
• 署名单位: Institute for Advanced Study - USA; Johannes Gutenberg University of Mainz; University of Minnesota System; University of Minnesota Twin Cities; Utah System of Higher Education; University of Utah; University of Nebraska System; University of Nebraska Lincoln
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0490-z
• 发表日期: 2014
• 页码: 509-519
• 关键词: characteristic p-greater-than-0

摘要

Let R be a commutative Noetherian ring that is a smooth -algebra. For each ideal of R and integer k, we prove that the local cohomology module 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.