On locally coherent hearts Article Swipe
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· 2017
· Open Access
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· DOI: https://doi.org/10.2140/pjm.2017.287.199
· OA: W2377735098
We show that, under particular conditions, if a t-structure in the unbounded\nderived category of a locally coherent Grothendieck category restricts to the\nbounded derived category of its category of finitely presented objects, then\nits heart is itself a locally coherent Grothendieck category. Those particular\nconditions are always satisfied when the Grothendieck category is arbitrary and\none considers the t-structure associated to a torsion pair in the category of\nfinitely presented objects. They are also satisfied when one takes any\ncompactly generated t-structure in the derived category of a commutative\nnoetherian ring which restricts to the bounded derived category of finitely\ngenerated modules. As a consequence, any t-structure in this latter bounded\nderived category has a heart which is equivalent to the category of finitely\npresented objects of some locally coherent Grothendieck category.\n