  Various classification theorems of thick subcategories of a triangulated
category have been obtained in many areas of mathematics. In this paper, as a
higher-dimensional version of the classification theorem of thick subcategories
of the stable category of finitely generated representations of a finite
$p$-group due to Benson, Carlson and Rickard, we consider classifying thick
subcategories of the stable category of Cohen-Macaulay modules over a
Gorenstein local ring. The main result of this paper yields a complete
classification of the thick subcategories of the stable category of
Cohen-Macaulay modules over a local hypersurface in terms of
specialization-closed subsets of the prime ideal spectrum of the ring which are
contained in its singular locus.
