TILTING, COTILTING, AND SPECTRA OF COMMUTATIVE NOETHERIAN RINGS

Abstract

We classify all tilting and cotilting classes over commutative noetherian rings in terms of descending sequences of specialization closed subsets of the Zariski spectrum. Consequently, all resolving subcategories of finitely generated modules of bounded projective dimension are classified.

We also relate our results to Hochster's Conjecture on the existence of finitely generated maximal Cohen-Macaulay modules.

Keywords

• Commutative noetherian ring
• tilting module
• cotilting module
• Zariski spectrum
• Cohen-Macaulay module