Related papers: Complete intersections and derived categories

We introduce the notions of Koszul $N$-complex, $\check{\mathrm{C}}$ech $N$-complex and telescope $N$-complex, explicit derived torsion and derived completion functors in the derived category $\mathbf{D}_N(R)$ of $N$-complexes using the…

We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…

The focus of this article is on metric completions of triangulated categories arising in the representation theory of hereditary finite dimensional algebras and commutative rings. We explicitly describe all completions of bounded derived…

We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general fibers smooth complete intersections, we prove the conjecture…

We study derived intersections of smooth analytic cycles, and provide in some cases necessary and sufficient conditions for this intersection be formal. In particular, if X is a complex submanifold of a complex manifold Y, we prove that X…

Let $D$ be a 2-dimensional regular local ring and let $Q(D)$ denote the quadratic tree of 2-dimensional regular local overrings of $D$. We examine the Noetherian rings that are intersections of rings in $Q(D)$. To do so, we describe the…

Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In…

This work concerns surjective maps $\varphi\colon R\to S$ of commutative noetherian local rings with kernel generated by a regular sequence that is part of a minimal generating set for the maximal ideal of $R$. The main result provides…

Given a set of objects $O$ in the plane, the corresponding intersection graph is defined as follows. Each object defines a vertex and an edge joins two vertices whenever the corresponding objects intersect. We study here the case of unit…

We introduce a class of noncommutatative algebras called representation complete intersections (RCI). A graded associative algebra A is said to be RCI provided there exist arbitrarily large positive integers n such that the scheme Rep_n(A),…

Let $R$ be a commutative noetherian ring with a dualizing complex. By recent work of Iyengar and Krause, the difference between the category of acyclic complexes and its subcategory of totally acyclic complexes measures how far $R$ is from…

In this article we prove that all the inclusions between the 'classical' and naturally defined full triangulated subcategories of a weakly approximable triangulated category are intrinsic (in one case under a technical condition). This…

We prove that the d\'evissage property holds for periodic cyclic homology for a local complete intersection embedding into a smooth scheme. As a consequence, we show that the complexified topological Chern character maps for the bounded…

Given a compactly generated triangulated category $\mathcal{T}$ equipped with an action of a graded-commutative Noetherian ring $R$, generalizing results of Letz, we prove a general result concerning the openness with respect to levels of…

We prove that the derived category of a smooth complete intersection variety is equivalent to a full subcategory of the derived category of a smooth projective Fano variety. This enables us to define some new invariants of smooth projective…

Let $R$ be a right notherian ring. We introduce the concept of relative singularity category $\Delta_{\mathcal{X}}(R)$ of $R$ with respect to a contravariantly finite subcategory $\mathcal{X}$ of $\rm{mod}\mbox{-}R.$ Along with some…

We prove that the dg category of perfect complexes on a smooth, proper Deligne-Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and proper. On the level of triangulated…

Let $R$ be a commutative ring and $I\subset R$ a finitely generated ideal. We discuss two definitions of derived $I$-adically complete (also derived $I$-torsion) complexes of $R$-modules which appear in the literature: the idealistic and…

We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…

In this short note we observe that the Serre functor on the residual category of a complete intersection can be easily described in the framework of hybrid models. Using this description we recover some recent results of Kuznetsov and…