Tilting, cotilting, and spectra of commutative noetherian rings

TL;DR

This paper classifies tilting and cotilting classes over commutative noetherian rings using spectral data, and connects these classifications to resolving subcategories and Hochster's conjecture on Cohen-Macaulay modules.

Contribution

It provides a comprehensive classification of tilting and cotilting classes via spectral sequences, linking them to resolving subcategories and Cohen-Macaulay module conjectures.

Findings

Classification of tilting and cotilting classes via specialization closed subsets

Resolution of subcategories of finitely generated modules with bounded projective dimension

Relation of results to Hochster's conjecture on Cohen-Macaulay modules

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.