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 ptorsion elements for every prime integer p, and consequently has infinitely many associated prime ideals.