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$$p$$-torsion elements in local cohomology modules. (English) Zbl 0965.13013
Author’s abstract: “For every prime integer $$p$$, M. Hochster conjectured the existence of certain $$p$$-torsion elements in a local cohomology module over a regular ring of mixed characteristic. We show that Hochster’s conjecture is false. We next construct an example where a local cohomology module over a hypersurface has $$p$$-torsion elements for every prime integer $$p$$, and consequently has infinitely many associated prime ideals”.

##### MSC:
 13D45 Local cohomology and commutative rings 13C12 Torsion modules and ideals in commutative rings
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