Related papers: Tensorial schemes

For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction implements an equivalence between the discrete category of morphisms Y --> X and the category of cocontinuous tensor functors…

Let K be an algebraically closed field, X a K-scheme, and X(K) the set of closed points in X. A constructible set C in X(K) is a finite union of subsets Y(K) for finite type subschemes Y in X. A constructible function f : X(K) --> Q has…

A classical approach to investigate a closed projective scheme $W$ consists of considering a general hyperplane section of $W$, which inherits many properties of $W$. The inverse problem that consists in finding a scheme $W$ starting from a…

Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this thesis we study constructions of cocomplete…

In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive- a coarse analogue of the notion of a functor on topological spaces being excisive. Further, taking cones, a coarsely excisive functor yields a…

We study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes. This is possible surprisingly often: we show that many of the standard examples of moduli stacks are determined by their…

We study Gorenstein categories. We show that such a category has Tate cohomological functors and Avramov-Martsinkovsky exact sequences connecting the Gorenstein relative, the absolute and the Tate cohomological functors. We show that such a…

We recall P. Balmer's definition of tensor triangular Chow group for a tensor triangulated category $\mathcal{K}$ and explore some of its properties. We give a proof that for a suitably nice scheme $X$ it recovers the usual notion of Chow…

Let $X$ be a fixed projective scheme which is flat over a base scheme $S$. The association taking a quasi-projective $S$-scheme $Y$ to the scheme parametrizing $S$-morphisms from $X$ to $Y$ is functorial. We prove that this functor…

We study two classes of morphisms in infinite type: tamely presented morphisms and morphisms with coherent pullback. These are generalizations of finitely presented morphisms and morphisms of finite Tor-dimension, respectively. The class of…

We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…

We compare tame actions in the category of schemes with torsors in the category of log schemes endowed with the log flat topology. We prove that actions underlying log flat torsors are tame. Conversely, starting from a tame cover of a…

We prove a few results about the map $Spc(F)$ induced on tensor-triangular spectra by a tensor-triangulated functor $F$. First, $F$ is conservative if and only if $Spc(F)$ is surjective on closed points. Second, if $F$ detects…

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…

Let f : Y -> X be a morphism of complex projective manifolds, and let F be a subsheaf of the tangent bundle which is closed under the Lie bracket, but not necessarily a foliation. This short paper contains an elementary and very geometric…

It is known that a linear system with a system matrix A constitutes a Hamiltonian system with a quadratic Hamiltonian if and only if A is a Hamiltonian matrix. This provides a straightforward method to verify whether a linear system is…

In this article, we first prove a general result in topology which states that every quasi-component of a quasi-spectral space is connected. \\ As an application, the structure of the connected components of every quasi-compact…

Let $X$ be a quasiprojective scheme. In this expository note we collect a series of useful structural results on the stack $\mathscr{C}oh^n(X)$ parametrising $0$-dimensional coherent sheaves of length $n$ over $X$. For instance, we discuss…

For topological spaces $X$ and $Y$, a (not necessarily continuous) function $f:X \rightarrow Y$ naturally induces a functor from the category of closed subsets of $X$ (with morphisms given by inclusions) to the category of closed subsets of…

We classify those rational maps $f: \mathbb{P}^1 \to \mathbb{P}^1$ for which there exists a contravariant tensor $q$ which is parallel, i.e. such that $f^*q // q$, by proving that such maps preserve a parabolic orbifold.