Jiaojiao Lu | Searcharxiv

arXiv2026

Compatibility of HRS tilt and completion of $t$-structures in triangulated categories

Let $K$ be a field, and $\mathcal{T}$ a $K$-linear essentially small triangulated category equipped with an extendable $t$-structure $(\mathcal{T}^{\leq0}, \mathcal{T}^{\geq0})$ with respect to a good metric $\mathfrak{B}$. Given a torsion class $\mathcal{X}$ in the heart of $(\mathcal{T}^{\leq0}, \mathcal{T}^{\geq0})$, we prove that lifting the HRS-tilt of $(\mathcal{T}^{\leq0}, \mathcal{T}^{\geq0})$ at $\mathcal{X}$ along the completion of $\mathcal{T}$ coincides with the HRS-tilt of the lifted $t$-structure at the completion of $\mathcal{X}$. As an application, we provide the compatibility result between left silting mutation in $\mathcal{T}$ and HRS tilting in the ambient completion.

math.CT↗

arXiv2022

Cofiniteness of generalized local cohomology modules for ideals of small dimension

Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$ and $M, N$ two finitely generated $R$-modules. By using a spectral sequence argument, it is shown that if either $\mathrm{dim}_RM\leq2$ and $\mathrm{H}^{i}_\mathfrak{a}(N)$ are $\mathfrak{a}$-cofinite for all $i\geq0$, or $\mathrm{H}^{i}_\mathfrak{a}(N)$ is an $\mathfrak{a}$-cofinite module of dimension $\leq1$ for each $i\geq1$, or $q(\mathfrak{a},R)\leq1$, then the $R$-modules $\mathrm{H}^{t}_\mathfrak{a}(M,N)$ are $\mathfrak{a}$-cofinite for all $t\geq0$.

math.AC↗