Related papers: A rapid introduction to Drinfeld modules, $t$-modu…

The aim of the paper is to provide a rather gentle introduction into Donaldson-Thomas theory using quivers with potential. The reader should be familiar with some basic knowledge in algebraic or complex geometry. The text contains many…

We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties…

In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing…

The aim of the paper is to classify the indecomposable modules and describe the Auslander--Reiten sequences for admissible algebras with formal two-ray modules.

We complete the proof of a Siegel type statement for finitely generated $\Phi$-submodules of $\mathbb{G}_a$ under the action of a Drinfeld module $\Phi$.

In this article we give application of closure operators in category of modules. Our main result shows that every subcategory A of injective modules of R-mod (under a mild condition) induces a torsion theory of R-mod.

We analyze the spectrum of the tensor-triangulated category of Artin-Tate motives over the base field R of real numbers, with integral coefficients. Away from 2, we obtain the same spectrum as for complex Tate motives, previously studied by…

In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.

These are notes of a series of talks about motivic integration I gave on the M\"unster Model Theory Month. Readers are assumed to have some basic knowledge of model theory and of valued fields. The notes are closest to the Cluckers-Loeser…

Let $T_R(M)$ be a tensor ring and $\mathcal{X}$, $\mathcal{Y}$ be two classes of $R$-modules. Under certain conditions, we prove that a $T_R(M)$-module $(A, u)$ is $Ind(\mathcal{X})$-Gorenstein projective if and only if $u$ is monomorphic…

We exhibit a connection between two constructions of twisted modules for a general vertex operator algebra with respect to inner automorphisms. We also study pseudo-derivations, pseudo-endomorphisms, and twist deformations of ordinary…

This article aims to explain essential elements of perturbation theory and their conceptual underpinnings. It is not meant as a summary of popular perturbation methods, though some illustrative examples are given to underline the main…

We obtain an equivariant class formula for z-deformation of t-modules. Under mild conditions, it allows us to get an equivariant class formula for t-modules.

We explore some concepts of module theory that derive from the notion of primeness, such as first modules, and extend them to more general environments. We also provide descriptions of simple left semiartinian rings, left local rings,…

We develop a theory of modulus triples, for future motivic applications.

The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduce and investigate the dual notions of r-submodules, n-submodules, and J-submodules of M.

We construct modular spaces of all 6-dimensional real semisimple Drinfeld doubles, i.e. the sets of all possible decompositions of the Lie algebra of the Drinfeld double into Manin triples. These modular spaces are significantly different…

In 1997 Richard Pink has clarified the concept of Hodge structures over function fields in positive characteristic, which today are called Hodge-Pink structures. They form a neutral Tannakian category over the underlying function field. He…

We prove a dynamical version of the Mordell-Lang conjecture in the context of Drinfeld modules. We use analytic methods similar to the ones employed by Skolem, Chabauty, and Coleman for studying diophantine equations.