Related papers: Cotilting Sheaves on Noetherian Schemes

We utilize the coherent-constructible correspondence to construct full strongly exceptional collections of nef line bundles in the derived category of a toric variety through the combinatorics of constructible sheaves built from polytopes.…

We determine the Chow ring (with Q-coefficients) of M_6 by showing that all Chow classes are tautological. In particular, all algebraic cohomology is tautological, and the natural map from Chow to cohomology is injective. To demonstrate the…

For a certain class of real analytic varieties with Lie group actions we develop a theory of (free-monodromic) tilting sheaves, and apply it to flag varieties stratified by real group orbits. For quasi-split real groups, we construct a…

In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p-local finite group in terms of representation rings of subgroups of its Sylow. We also prove a stable elements…

We present an alternative construction of Soergel's category of bimodules associated to a reflection faithful representation of a Coxeter system. We show that its objects can be viewed as sheaves on the associated moment graph. We introduce…

We propose notions of "Noetherian" and "integral" for schemes over an abelian symmetric monoidal category $(\mathcal C,\otimes,1)$. For Noetherian integral schemes, we construct a "function field" that is a commutative monoid object of…

For a semi-separated noetherian scheme, we show that the category of cotorsion Gorenstein flat quasi-coherent sheaves is Frobenius and a natural non-affine analogue of the category of Gorenstein projective modules over a noetherian ring. We…

We put a monoidal model category structure on the category of chain complexes of quasi-coherent sheaves over a quasi-compact and semi-separated scheme X. The approach generalizes and simplifies methods used by the author to build monoidal…

A natural generalization of locally noetherian and locally coherent categories leads us to define locally type $FP_{\infty}$ categories. They include not just all categories of modules over a ring, but also the category of sheaves over any…

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…

We show that on integral normal separated schemes whose function field is separably closed, for each pair of points the intersection of the resulting local schemes is local. This extends a result of Artin from rings to schemes. The argument…

For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect…

The Brill-Noether theory of curves plays a fundamental role in the theory of curves and their moduli and has been intensively studied since the 19th century. In contrast, Brill-Noether theory for higher dimensional varieties is less…

This paper focuses on the study of a new category of vector bundles. The objects of this category, called chiral vector bundles, are pairs given by a complex vector bundle along with one of its automorphisms. We provide a classification for…

We revisit a construction of wide subcategories going back to work of Ingalls and Thomas. To a torsion pair in the category $ R\operatorname{-}\operatorname{mod}$ of finitely presented modules over a left artinian ring $R$, we assign two…

We prove that the exactness of direct limits in an abelian category with products and an injective cogenerator J is equivalent to a condition on J which is well-known to characterize pure-injectivity in module categories, and we describe an…

Let $\mathbb{X}$ be a weighted projective line of tubular type and $\operatorname{coh}\mathbb{X}$ the category of coherent sheaves on $\mathbb{X}$. The main purpose of this note is to show that the subgraph of the tilting graph consisting…

For the cluster category of a hereditary or a canonical algebra, equivalently for the cluster category of the hereditary category of coherent sheaves on a weighted projective line, we study the Grothendieck group with respect to an…

Let $\mathcal{H}$ be a connected hereditary abelian category with tilting objects. It is proved that the cluster-tilting graph associated with $\mathcal{H}$ is always connected. As a consequence, we establish the connectedness of the…

For a commutative noetherian ring R, we investigate relations between tilting and cotilting modules in Mod-R and Mod-R_m where m runs over the maximal spectrum of R. For each finite n, we construct a 1-1 correspondence between (equivalence…