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## Multi angle  Local cohomology modules of a smooth $\mathbb{Z}-algebra$ have a finite number of associated primes Lyubeznik, Gennady (Auteur de la Conférence) | CIRM (Editeur )

Let $R$ be a commutative Noetherian ring that is a smooth $\mathbb{Z}-algebra$. For each ideal $a$ of $R$ and integer $k$, we prove that the local cohomology module $H^k_a(R)$ 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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