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arXiv · 1304.4692

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

Bhargav Bhatt·Manuel Blickle·Gennady Lyubeznik·Anurag K. Singh·Wenliang Zhang
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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.

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Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, Wenliang Zhang. 2013-12-19. Local cohomology modules of a smooth Z-algebra have finitely many associated primes. https://doi.org/10.1007/s00222-013-0490-z

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