$p$-torsion elements in local cohomology modules

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.

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Published 1 January 2000