Wide subcategories over commutative coherent rings

Abstract

In this paper, we mainly prove Hovey's conjecture: for any commutative coherent ring, there is a lattice isomorphism between the lattice of wide subcategories of the category of finitely presented modules and that of thick subcategories of the perfect derived category. We construct, for every finitely presented module, a bounded finite free complex whose zeroth homology is the given module and whose homology lies in its abelian closure. This realization gives an inverse to Hovey's correspondence without a closure operation. In addition, we study finite extension filtrations, their behavior under change of rings, and the limits of reconstructing wide subcategories of arbitrary modules from finitely presented modules.