Related papers: Bounding ramification with coherent sheaves

We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…

We describe a differential graded Lie algebra controlling infinitesimal deformations of triples $(X,\mathcal{F},\sigma)$, where $\mathcal{F}$ is a coherent sheaf on a smooth variety $X$ over a field of characteristic 0 and $\sigma\in…

This paper is the first in a series of papers in which we define and study a category of "sheaves of $\mathcal Z$-modules on the set of alcoves" that carries important information on the category of representations of semisimple Lie…

We give a generalization, in the context of sheaves, of a classical result of Grothendieck concerning the integrability of connections of type $(0,1)$ over a ${\cal C}^{\infty}$ vector bundle over a complex manifold. We introduce the notion…

We prove that intermediate extensions of perverse constructible $\mathbb{F}_p$-sheaves commute with smooth pullbacks for schemes admitting a closed embedding into a smooth scheme over a field of characteristic $p$ (embeddable schemes for…

We use Kiehl-Verdier's and Houzel's finiteness theorems in the setting of local analytic geometry, and the Whitney-Thom theory of stratified spaces, to prove that fibrewise constructible complex of sheaves have coherent direct images. We…

Inspired by the homological mirror symmetry conjecture of Kontsevich, we construct new classes of automorphisms of the bounded derived category of coherent sheaves on a smooth Calabi-Yau variety.

A correspondence between quasicoherent sheaves on toric schemes and graded modules over some homogeneous coordinate ring is presented, and the behaviour of several finiteness properties under this correspondence is investigated.

Let $X$ be a projective variety over a field. In this paper, we will construct a moduli space of very ample line bundles on $X$. In doing so, we develop a generalization of Fitting ideals to complexes of sheaves on $X$. We give other…

We show that the cohomology table of any coherent sheaf on projective space is a convergent--but possibly infinite--sum of positive real multiples of the cohomology tables of what we call supernatural sheaves.

We construct generalized Weyman complexes for coherent sheaves on projective space and describe explicitly how the differential depend on the differentials in the correpsonding Tate resolution. We apply this to define the Weyman complex of…

Let X be a scheme of finite type over a Noetherian base scheme S admitting a dualizing complex, and let U be an open subset whose complement has codimension at least 2. We extend the Deligne-Bezrukavnikov theory of perverse coherent sheaves…

For an abelian category and a distinguished object with a graded endomorphism ring a necessary and sufficient criterion is given so that the category is equivalent to the abelian quotient of the category of finitely presented graded modules…

In this paper, we shall consider some finiteness of ind-sheaves with ring actions. As the main result of this paper, there exists an equivalence of categories between the abelian category of coherent ind-$\beta\mathcal{A}$-modules and the…

We introduce new enhancements for the bounded derived category $D^b(Coh(X))$ of coherent sheaves on a suitable scheme $X$ and for its subcategory $Perf(X)$ of perfect complexes. They are used for translating Fourier-Mukai functors to…

We prove that the categories of coherent sheaves over weighted projective lines of tubular type are explicitly related to each other via the equivariantization with respect to certain cyclic group actions.

Improved local and global versions of the effective Nullstellensatz for ideal sheaves on non-singular complex varieties are obtained, based on a new invariant motivated by the notion of finite type from the theory of several complex…

We prove new homological stability results for general linear groups over finite fields. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category of $E_\infty$-algebras, guided…

Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on…

In this note we relate three topics for arithmetic schemes: a general duality for \'etale constructible torsion sheaves, an \'etale homology theory, and a Gersten-Bloch-Ogus-Kato complex. The results in this paper have been used in other…