The 𝑡-structure induced by an 𝑛-tilting module

Bazzoni, Silvana

doi:10.1090/tran/7488

The $t$-structure induced by an $n$-tilting module
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Trans. Amer. Math. Soc. 371 (2019), 6309-6340 Request permission

Abstract:

We study the $t$-structure induced by an $n$-tilting module $T$ in the derived category $\mathcal {D}(R)$ 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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