Related papers: Continuous closure of sheaves
We study torsion free sheaves on integral projective curves with at most ordinary cusps as singularities. Adjusting Seshadri's structure from the nodal case to this one, we describe these sheaves by means of a triple defined in the…
We develop persistent homology in the setting of filtrations of (Cech) closure spaces. Examples of filtrations of closure spaces include metric spaces, weighted graphs, weighted directed graphs, and filtrations of topological spaces. We use…
Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can…
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.
Starting from Sinclair's 1976 work {\it Automatic Continuity of Linear Operators}, Cambridge University Press, (1976), on automatic continuity of linear operators on Banach spaces, we prove that sequences of intertwining continuous linear…
We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a…
We provide a stacky fan description of the total space of certain split vector bundles, as well as their projectivization, over toric Deligne-Mumford stacks. We then specialize to the case of Hirzebruch orbifold $\mathcal{H}_{r}^{ab}$…
A Cech closure space $(X,u)$ is a set $X$ with a (Cech) closure operator $u$ which need not be idempotent. Many properties which hold in topological spaces hold in Cech closure spaces as well. The notions of proper (splitting) and…
We study the geometry of the moduli stack of torsion-free sheaves on ribbons. We introduce a stratification of the stack by the complete type of the sheaves, and we investigate the geometric properties of the strata and their closure…
Given a quasi-projective scheme M over complex numbers equipped with a perfect obstruction theory and a morphism to a nonsingular quasi-projective variety B, we show it is possible to find an affine bundle M'/ M that admits a perfect…
It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a…
We prove, for quasicompact separated schemes over ground fields, that Cech cohomology coincides with sheaf cohomology with respect to the Nisnevich topology. This is a partial generalization of Artin's result that for noetherian schemes…
Motivated by the problem of finding algebraic constructions of finite coverings in commutative algebra, the Steinitz realization problem in number theory, and the study of Hurwitz spaces in algebraic geometry, we investigate the vector…
The higher direct image complex of a coherent sheaf (or finite complex of coherent sheaves) under a projective morphism is a fundamental construction that can be defined via a Cech complex or an injective resolution, both inherently…
Let $F$ be a torsionfree semistable coherent sheaf on a polarized normal projective variety. We prove that $F$ has a unique maximal locally free subsheaf $V$ such that $F/V$ is torsionfree and $V$ admits a filtration of subbundles for which…
We show that faithfully flat smooth extensions are reduced flat, and therefore, fit into the Jacobi-Zariski exact sequence in Hochschild homology and cyclic (co)homology even when the algebras are noncommutative or infinite dimensional. We…
We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…
A conjecture of Huneke and Wiegand claims that, over one-dimensional commutative Noetherian local domains, the tensor product of a finitely generated, non-free, torsion-free module with its algebraic dual always has torsion. Building on a…
We axiomatize the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalized automorphic sheaf is proposed which includes sheaves of (meromorphic) sections…
We develop a theory of sheaves and cohomology on the category of proper modulus pairs. This complements [KMSY21], where a theory of sheaves and cohomology on the category of non-proper modulus pairs has been developed.