Geodesic
Hearts for commutative Noetherian rings: torsion pairs and derived equivalences
Documenta mathematica, Tome 26 (2021), pp. 829-871.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Over a commutative noetherian ring $R$, the prime spectrum controls, via the assignment of support, the structure of both $\mathsf{Mod}(R)$ and $\mathsf{D}(R)$. We show that, just like in $\mathsf{Mod}(R)$, the assignment of support classifies hereditary torsion pairs in the heart of any nondegenerate compactly generated $t$-structure of $\mathsf{D}(R)$. Moreover, we investigate whether these $t$-structures induce derived equivalences, obtaining a new source of Grothendieck categories which are derived equivalent to $\mathsf{Mod}(R)$.
Classification : 13D30, 13D09, 18E10, 18G80
Keywords: support, derived equivalence, HRS-tilting, hereditary torsion pairs, commutative Noetherian ring 
@article{DOCMA_2021__26__a33,
     author = {Pavon, Sergio and Vit\'oria, Jorge},
     title = {Hearts for commutative {Noetherian} rings: torsion pairs and derived equivalences},
     journal = {Documenta mathematica},
     pages = {829--871},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a33/}
}
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Pavon, Sergio; Vitória, Jorge. Hearts for commutative Noetherian rings: torsion pairs and derived equivalences. Documenta mathematica, Tome 26 (2021), pp. 829-871. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a33/