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Govorov--Lazard and finite deconstructibility for Gorenstein and restricted homological dimensions
Souvik Dey, Michal Hrbek, Giovanna Le Gros
Over Cohen--Macaulay rings admitting a pointwise dualizing module, we show that the class of modules of restricted projective dimension bounded by any integer is finitely deconstru…
Cotorsion pairs and Tor-pairs over commutative noetherian rings
Dolors Herbera, Michal Hrbek, Giovanna Le Gros
For a commutative noetherian ring , we classify all the hereditary cotorsion pairs cogenerated by pure-injective modules of finite injective dimension. The classification is don…
The finite type of modules of bounded projective dimension and Serre's conditions
Michal Hrbek, Giovanna Le Gros
Let be a commutative noetherian ring. We prove that the class of modules of projective dimension bounded by is of finite type if and only if satisfies Serre's condition…
Restricted injective dimensions over Cohen-Macaulay rings
Michal Hrbek, Giovanna Le Gros
We show that the small and large restricted injective dimensions coincide for Cohen-Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of Sath…
Silting, cosilting, and extensions of commutative ring
Simion Breaz, Michal Hrbek, George Ciprian Modoi
We study the transfer of (co)silting objects in derived categories of module categories via the extension functors induced by a morphism of commutative rings. It is proved that the…
Gluing compactly generated t-structures over stalks of affine schemes
Michal Hrbek, Jiangsheng Hu, Rongmin Zhu
We show that compactly generated t-structures in the derived category of a commutative ring are in a bijection with certain families of compactly generated t-structures over th…