Mathematical Research Letters
Volume 7 (2000)
$p$-torsion elements in local cohomology modules
Pages: 165 – 176
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.