Related papers: Sheafification of linear functors

Given an algebraic stack $X$, one may compare the derived category of quasi-coherent sheaves on $X$ with the category of dg-modules over the dg-ring of functions on $X$. We study the analogous question in stable homotopy theory, for derived…

We characterise those objects in the derived category of a scheme which are a sheaf supported on a closed subscheme in terms of Koszul complexes. This is applied to generalize to arbitrary schemes the fully faithfullness criteria of an…

Given a graded monoid A with 1, one can construct a projective monoid scheme MProj(A) analogous to Proj(R) of a graded ring R. This paper is concerned with the study of quasicoherent sheaves (of pointed sets) on MProj(A), and we prove…

The contribution of this article is quadruple. It (1) unifies various schemes of premodels/models including situations such as presheaves/sheaves, sheaves/flabby sheaves, prespectra/$\Omega$-spectra, simplicial topological spaces/(complete)…

In 1984, Charney and Lee defined a category of stable curves and exhibited a rational homology equivalence from its geometric realisation to (the analytification of) the moduli stack of stable curves, also known as the…

In this article, we develop an explicit categorical realization of sheafification based on colimits, products, and subobjects, emphasizing its behavior in algebraic and topological-algebraic settings. We prove that if $\mathcal{C}$ is a…

We show that, under appropriate hypothesis, the groupoid of maps from S to an an algebraic stack X can be identified with a category of tensor functors from coherent sheaves on X to coherent sheaves on S. As an application, we show that if…

We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation,…

Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…

We study a category of semiinfinite sheaves on the affine flag variety of a connected reductive algebraic group, with coefficients in a field of arbitrary characteristic, generalizing some results of Gaitsgory and showing that this category…

We consider a central extension of the sheaf of Lie algebras of maps from a manifold into a finite-dimensional simple Lie algebra, together with the sheaf of vector fields. Using vertex algebra methods we construct sheaves of modules for…

We show that for a quasicompact quasiseparated scheme $X$, the following assertions are equivalent: (1) the category $\operatorname{QCoh}(X)$ of all quasicoherent sheaves on $X$ has a flat generator; (2) for every injective object $\mathcal…

Partial difference operators for a large class of functors between presheaf categories are introduced, extending our difference operator from \cite{Par24} to the multivariable case. These combine into the Jacobian profunctor which provides…

This paper considers generalizations of certain arithmetic complexes appearing in the work of Raicu and VandeBogert in connection with the study of stable sheaf cohomology on flag varieties. Defined over the ring of integer valued…

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1 and multiplicity 6. We decompose their moduli spaces into strata which occur naturally as quotients modulo actions of certain algebraic…

The first author recently introduced a "nearby cycles formalism" in the framework of chain complexes of parity sheaves. In this paper, we compute this functor in two related settings: (i) affine space, stratified by the action of a torus,…

We introduce frameworks for constructing global derived moduli stacks associated to a broad range of problems, bridging the gap between the concrete and abstract conceptions of derived moduli. Our three approaches are via differential…

The central aim of this monograph is to provide decomposition results for quasi-coherent sheaves on the moduli stack of one-dimensional formal groups. These results will be based on the geometry of the stack itself, particularly the height…

In this note we study symmetric monoidal functors from a symmetric monoidal 1-category to a cartesian symmetric monoidal $\infty$-category, which are in addition hypersheaves for a certain topology. We prove a symmetric monoidal version of…

We give a long exact sequence for the homology of a graded atomic lattice equipped with a sheaf of modules, in terms of the deleted and restricted lattices. This is then used to compute the homology of the arrangement lattice of a…