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

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 $H_I^k(R)$ 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.

Cited by in corpus (3)

• Cohomological dimension of ideals defining Veronese subrings
• Associated primes of Local cohomology modules over Regular rings
• The level of pairs of polynomials