Let R be a commutative Noetherian ring that is a smooth ℤ-algebra. For each ideal a of R and integer k, we prove that the local cohomology module Hak(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.
This video was produced by CIRM as part of the conference Commutative algebra and its interactions with algebraic geometry.
