Tilting Modules and Tilting Torsion Pairs

Mattiello, Francesco; Pavon, Sergio; Tonolo, Alberto

doi:10.1007/978-3-030-43416-8_18

Cited by 2 publications

(1 citation statement)

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“…The properties of this new t-structure depend on the properties of the given torsion pair, and therefore one may say that studying HRS-tilts often can be reduced to studying the associated torsion pairs. However, HRS-tilts turn out to be an elementary operation that, when iterated, allows us obtain a large class of t-structures (see, for example, [16,32]). Moreover, HRS-tilts turn out to play an important role in understanding Bridgeland's stability condition manifold (see, for example, [10], [11] and [38]).…”

Section: Introductionmentioning

confidence: 99%

Hearts for commutative Noetherian rings: torsion pairs and derived equivalences

Pavon

Vitória

2021

Doc. Math.

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Over a commutative noetherian ring R, the prime spectrum controls, via the assignment of support, the structure of both Mod(R) and D(R). We show that, just like in Mod(R), the assignment of support classifies hereditary torsion pairs in the heart of any nondegenerate compactly generated t-structure of D(R). Moreover, we investigate whether these t-structures induce derived equivalences, obtaining a new source of Grothendieck categories which are derived equivalent to Mod(R).

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