Related papers: Proper morphisms of $\infty$-topoi
This note is concerned with quasi-perfect morphisms between Noetherian algebraic spaces. In particular, we study the local behavior of quasi-perfect proper morphisms. We show that quasi-perfectness of a proper morphism can be detected at…
We develop the theory of exact completions of regular $\infty$-categories, and show that the $\infty$-categorical exact completion (resp. hypercompletion) of an abelian category recovers the connective half of its bounded (resp. unbounded)…
We take a novel lattice-theoretic approach to the $\tau$-cluster morphism category $\mathfrak{T}(A)$ of a finite-dimensional algebra $A$ and define the category via the lattice of torsion classes $\mathrm{tors } A$. Using the lattice…
We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective…
We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by algebraic maps for the compact-open topology. This theorem can…
The purpose of this paper is finding the essential attributes underlying the convexity theorems for momentum maps. It is shown that they are of topological nature; more specifically, we show that convexity follows if the map is open onto…
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…
We extend the classical (connected, etale) factorization of locally connected geometric morphisms into a (terminally connected, pro-etale) factorization for all geometric morphisms between Grothendieck topoi. We discuss properties of both…
A map $f:X\to Y$ between topological spaces is skeletal if the preimage $f^{-1}(A)$ of each nowhere dense subset $A\subset Y$ is nowhere dense in $X$. We prove that a normal functor $F:Comp\to Comp$ is skeletal (which means that $F$…
We introduce the notion of a geometric $(\infty,1)$-category, the protopyical example of which is an $(\infty,1)$-topos. We study (hyper)sheaves on geometric $(\infty,1)$-categories, proving that these are characterized by a form of…
The Local-to-Global-Principle used in the proof of convexity theorems for momentum maps has been extracted as a statement of pure topology enriched with a structure of convexity. We extend this principle to not necessarily closed maps…
One fundamental consequence of a scheme $X$ being proper is that the functor classifying maps from $X$ to any other suitably nice scheme or algebraic stack is representable by an algebraic stack. This result has been generalized by…
In the context of relative topos theory via stacks, we introduce the notion of existential fibred site and of existential topos of such a site. These notions allow us to develop relative topos theory in a way which naturally generalizes the…
We give a framework to produce constructible functions from natural functors between categories, without need of a morphism of moduli spaces to model the functor. We show using the Riemann-Hilbert correspondence that any natural (derived)…
The main objective of this paper is to show that the homotopy colimit of a diagram of quasi-categories and indexed by a small category is a localization of Lurie's higher Grothendieck construction of the diagram. We thereby generalize…
We demonstrate that categories of continuous actions of topological monoids on discrete spaces are Grothendieck toposes. We exhibit properties of these toposes, giving a solution to the corresponding Morita-equivalence problem. We…
We give geometric characterisations of patch and Lawson topologies in the context of predicative point-free topology using the constructive notion of located subset. We present the patch topology of a stably locally compact formal topology…
We introduce and study the proper topological complexity of a given configuration space, a version of the classical invariant for which we require that the algorithm controlling the motion is able to avoid any possible choice of ``unsafe''…
Let $f,g:X \to Y$ be continuous mappings. We say that $f$ is topologically equivalent to $g$ if there exist homeomorphisms $\Phi : X\to X$ and $\Psi: Y\to Y$ such that $\Psi\circ f\circ \Phi=g.$ Let $X,Y$ be complex smooth irreducible…
To a dominant morphism $X/S \to Y/S$ of N\oe therian integral $S$-schemes one has the inclusion $C_{X/Y}\subset B_{X/Y}$ of the critical locus in the branch locus of $X/Y$. Starting from the notion of locally complete intersection…