Local cohomology modules of a smooth mathbb{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 $H^k_I(R)$ 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.
 Publication:

Inventiones Mathematicae
 Pub Date:
 September 2014
 DOI:
 10.1007/s002220130490z
 arXiv:
 arXiv:1304.4692
 Bibcode:
 2014InMat.197..509B
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 Primary 13D45;
 Secondary 13F20;
 14B15;
 13N10;
 13A35
 EPrint:
 doi:10.1007/s002220130490z