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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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