|
Abstract:
The tight closure operation of Hochster and Huneke associates to each ideal I, in a Noetherian domain of finite
characteristic p, an ideal I* that contains I. Whether tight closure commutes
with localization with respect to a multiplicative subset was a long-standing open question. Last year, Holger Brenner
saw how an obscure paper of mine, consisting of intricate matrix calculations, and apparently unrelated to tight closure,
suggested the falseness of this "localization conjecture". He and I then produced a counterexample; I'll describe our
discovery. In addition to matrix calculations connected to Hilbert-Kunz theory, we use results of Hochster
and Huneke relating the "test ideal" for tight closure to local cohomology.
|