4 papers · 1 filter
On Takahashi's descent question about dominant local rings
Jian Liu
This article studies dominant local rings, a notion introduced by Takahashi. We prove that, for a flat local homomorphism R-->S between commutative noetherian local rings, dominanc…
Pretriangulated categories failing (TR4)
Xiao-Wu Chen, Jian Liu, Sergei O. Ivanov +3
We introduce gemstones in a pretriangulated category, which are used to perturb pretriangulated structures. For a triangulated category whose stable category of cohere…
Khovanov homology: pro-tangles, derived colimits and spectral sequences
Jian Liu, Kefeng Liu, Li Shen
This paper introduces \emph{pro-tangles}, a natural generalization of classical tangles, which are functors from the Boolean cube to Bar-Natan's cobordism category. By employing th…
Cotorsion pairs, thick subcategories, and finitely generated Gorenstein projective modules
Souvik Dey, Jian Liu, Xue-Song Lu
Let be a noetherian algebra over a Cohen--Macaulay ring admitting a canonical module , and assume that is maximal Cohen--Macaulay over . We prove that the categor…