Homological epimorphisms, compactly generated t-structures and Gorenstein-projective modules

Abstract

The aim of this paper is two-fold. Given a recollement (T′, T, T″, i*, i _*, i ^!, j _!, j*, j _*), where T′, T, T″ are triangulated categories with small coproducts and T is compactly generated. First, the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i _* preserves compact objects. As a con-sequence, given a ladder (T′, T, T″, T, T′) of height 2, then the certain BBD-induction of compactly generated t-structures is compactly generated. The authors apply them to the recollements induced by homological ring epimorphisms. This is the first part of their work. Given a recollement (D(B-Mod),D(A-Mod),D(C-Mod), i*, i _*, i ^!, j _!, j*, j _*) induced by a homological ring epimorphism, the last aim of this work is to show that if A is Gorenstein, _A B has finite projective dimension and j _! restricts to D ^b(C-mod), then this recollement induces an unbounded ladder (B- G proj,A- G proj, C- G proj) of stable categories of finitely generated Gorenstein-projective modules. Some examples are described.

Keywords

Compactly generated t-structure / Recollement / BBD-induction / BPP-induction / Homological ring epimorphism / Gorenstein-projective module

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