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

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