Related papers: Derived Equivalence induced by $n$-tilting modules

We introduce the notion of balanced pair of additive subcategories in an abelian category. We give sufficient conditions under which the balanced pair of subcategories gives rise to equivalent homotopy categories of complexes. As an…

Let $R$ be a ring and $T \in {\rm Mod-}R$ be a (non-classical) tilting module of finite projective dimension. Let $\mathcal T=({\mathcal T}^{\leq0}, {\mathcal T}^{\geq0})$ be the $t$-structure on $D(R)$ generated by $T$ and ${\mathcal…

We give a direct proof of the following known result: the Grothendieck group of a triangulated category with a silting subcategory is isomorphic to the split Grothendieck group of the silting subcategory. Moreover, we obtain its…

We consider the smallest triangulated subcategory of the unbounded derived module category of a ring that contains the injective modules and is closed under set indexed coproducts. If this subcategory is the entire derived category, then we…

We show that if a (not necessarily algebraic) triangulated category T contains an admissible hereditary abelian subcategory H, then we can lift the inclusion of H into T to a fully faithful triangle functor from the whole of the bounded…

We propose a solution to the "curvature problem" from arXiv:1505.03698 and arXiv:0905.3845 for infinitesimal deformations. Let $k$ be a field, $A$ a dg algebra over $k$ and $A_n = A[t]/(t^{n+1})$ a cdg algebra over $R_n = k[t]/(t^{n+1})$,…

Let $U'_q(\mathfrak{g})$ be a twisted affine quantum group of type $A_{N}^{(2)}$ or $D_{N}^{(2)}$ and let $\mathfrak{g}_{0}$ be the finite-dimensional simple Lie algebra of type $A_{N}$ or $D_{N}$. For a Dynkin quiver of type…

We show that every two-term tilting complex over an Artin algebra has a tilting module over a certain factor algebra as a homology group. Also, we determine the endomorphism algebra of such a homology group, which is given as a certain…

We prove that a coherent DQ-kernel induces an equivalence between the derived categories of DQ-modules with coherent cohomology if and only if the graded commutative kernel associated to it induces an equivalence between the derived…

We classify all tilting classes over an arbitrary commutative ring via certain sequences of Thomason subsets of the spectrum, generalizing the classification for noetherian commutative rings by…

We investigate the triangulated hull of the orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension functor. It turns out that the triangulated hull will correspond…

For any CDG-ring $B^\bullet=(B^*,d,h)$, we show that the homotopy category of graded-projective (left) CDG-modules over $B^\bullet$ is equivalent to the quotient category of the homotopy category of graded-flat CDG-modules by its full…

In [arXiv:1509.02937], the notion of a module tensor category was introduced as a braided monoidal central functor $F\colon \mathcal{V}\longrightarrow \mathcal{T}$ from a braided monoidal category $\mathcal{V}$ to a monoidal category…

We study aisles in the derived category of a hereditary abelian category. Given an aisle, we associate a sequence of subcategories of the abelian category by considering the different homologies of the aisle. We then obtain a sequence,…

We formulate a Beilinson-Bernstein type derived equivalence for a quantized enveloping algebra at a root of 1 as a conjecture. It says that there exists a derived equivalence between the category of modules over a quantized enveloping…

Given a ring homomorphism $B \to A$, consider its centralizer $R = A^B$, bimodule endomorphism ring $S = \End {}_BA_B$ and sub-tensor-square ring $T = (A \o_B A)^B$. Nonassociative tensoring by the cyclic modules $R_T$ or ${}_SR$ leads to…

Following Mitchell's philosophy, in this paper we define the analogous of the triangular matrix algebra to the context of rings with several objects. Given two additive categories $\mathcal{U}$ and $\mathcal{T}$ and $M\in…

Making use of Freyd's free abelian category on a preadditive category we show that if $T:D\rightarrow \mathcal{A}$ is a representation of a quiver $D$ in an abelian category $\mathcal{A}$ then there is an abelian category $\mathcal{A} (T)$,…

Let $\Lambda $ be an artin algebra and $T$ a $\tau$-tilting $\Lambda$-module. We prove that $T$ is a tilting module if and only if ${\rm Ext}_{\Lambda}^{i}(T,\Fac T)=0$ for all $i\geq 1$, where $\Fac T$ is the full subcategory consisting of…

It is shown that, modulo an equivalence relation induced by finite correspondences preserving Cantor rank, the class of topological spaces is an integral semi-ring on which the Cantor derivative is precisely a derivation.