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.
The t-structure induced by an n-tilting module
Silvana Bazzoni
2019
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.
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