Related papers: Frobenius-Perron theory for projective schemes

A noncommutative deformation of a quadric surface is usually described by a three-dimensional cubic Artin-Schelter regular algebra. In this paper we show that for such an algebra its bounded derived category embeds into the bounded derived…

We present the concept of cotorsion pairs cut along subcategories of an abelian category. This provides a generalization of complete cotorsion pairs, and represents a general framework to find approximations restricted to certain…

A double category of relations is essentially a cartesian equipment with strong, discrete and functorial tabulators and for which certain local products satisfy a Frobenius Law. A double category of relations is equivalent to a double…

In this paper we introduce a new approach to determinant functors which allows us to extend Deligne's determinant functors for exact categories to Waldhausen categories, (strongly) triangulated categories, and derivators. We construct…

A pair of adjoint functors $(F,G)$ is called a Frobenius pair of the second type if $G$ is a left adjoint of $\beta F\alpha$ for some category equivalences $\alpha$ and $\beta$. Frobenius ring extensions of the second kind provide examples…

We exhibit a canonical equivalence between the hermitian $K$-theory (alias Grothendieck-Witt) spectrum of an exact form category and that of its derived Poincar\'e $\infty$-category, with no assumptions on the invertibility of $2$. Along…

Integral modular categories of Frobenius-Perron dimension $pq^n$, where $p$ and $q$ are primes, are considered. It is already known that such categories are group-theoretical in the cases of $0 \leq n \leq 4$. In the general case we…

We present a dynamical approach to the classical Perron-Frobenius theory by using some elementary knowledge on linear ODEs. It is completely self-contained and significantly different from those in the literature. As a result, we develop a…

Let X be a smooth projective curve of genus g>1 over an algebraically closed field of characteristic 2. Pull-back by the (absolute) Frobenius on X only defines a rational morphism on the moduli scheme of rank-2 vector bundles on X, because…

Let $(1)$ be an automorphism on an additive category $\mathcal{B}$, and let $\eta\colon (1)\to {\rm Id}_{\mathcal{B}}$ be a natural transformation satisfying $\eta_{X(1)}=\eta_X(1)$ for any object $X$ in $\mathcal{B}$. We construct a new…

We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…

We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are particularly…

We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently…

We show that induction along a Frobenius extension of Hopf algebras is a Frobenius monoidal functor in great generality, in particular, for all finite-dimensional and all pointed Hopf algebras. As an application, we show that induction…

We study the geometry and partial differential equations arising from the consideration of Frobenius determinants, also called-group-determinants. This leads us to address some aspects of twistor theory as well as some extensions of Bessel…

We classify the invariant Borel measures for adic transformations, where the alphabets have bounded size and the measure is finite on the path space of some sub-Bratteli diagram. We develop a nonstationary version of the Frobenius normal…

We show that the Frobenius and Verschiebung maps that are fundamental to Witt vectors lift to the reduced K-theory of endomorphisms. In particular, we define Frobenius and Verschiebung maps for the reduced K-theory of twisted endomorphisms…

Torsion theories play an important role in abelian categories and they have been widely studied in the last sixty years. In recent years, with the introduction of pretorsion theories, the definition has been extended to general…

Consider a locally cartesian closed category with an object I and a class of trivial fibrations, which admit sections and are stable under pushforward and retract as arrows. Define the fibrations to be those maps whose Leibniz exponential…

It is shown that for certain maps, including concave maps, on the $d$-dimensional lattice of positive integer points, 'approximate' eigenvectors can be found. Applications in epidemiology as well as distributed resource allocation are…