The t-structure induced by an n-tilting module

Abstract

We study the t-structure induced by an n-tilting module T in the derived category D(R) of a ring R. Our main objective is to determine when the heart of the t-structure is a Grothendieck category. We obtain characterizations in terms of properties of the module category over the endomorphism ring of T and as a main result we prove that the heart is a Grothendieck category if and only if T is a pure projective $R$-module.

Cited by in corpus (5)

• The tilting-cotilting correspondence
• $t$-Structures on stable derivators and Grothendieck hearts
• $t$-Structures with Grothendieck hearts via functor categories
• Tilting modules and tilting torsion pairs - filtrations induced by tilting modules
• Fishing for complements