Related papers: Classification of Rank 6 Modular Categories with G…
The Hodge Galois group is the Tannakian Galois group of the category of real mixed Hodge structures. It has a subgroup, called the twistor Galois group, which is the Galois group of the category of mixed twistor structures, defined by C.…
We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of…
We classify rigid local systems of rank 7 whose monodromy group is dense in the simple algebraic group of type G2. This leads to motives with Galois group G2.
We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We…
Starting with a symmetric monoidal adjunction with certain properties, one derives another symmetric monoidal adjunction with the same properties between the respective categories of all V-categories. If one begins with a reflection of a…
We study good (i.e., semisimple) reductions of semisimple rigid tensor categories modulo primes. A prime p is called good for a semisimple rigid tensor category C if such a reduction exists (otherwise, it is called bad). It is clear that a…
We investigate invertible elements and gradings in braided tensor categories. This leads us to the definition of theta-, product-, subgrading and orbitcategories in order to construct new families of BTC's from given ones. We use the…
Instead of studying anyon condensation in concrete models, we take an abstract approach. Assume that a system of anyons, which form a modular tensor category D, is obtained via an anyon condensation from another system of anyons (i.e.…
The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…
Canonical Polyadic Decomposition (CPD) of a higher-order tensor is decomposition in a minimal number of rank-1 tensors. We give an overview of existing results concerning uniqueness. We present new, relaxed, conditions that guarantee…
$N$-Metaplectic categories, unitary modular categories with the same fusion rules as $SO(N)_2$, are prototypical examples of weakly integral modular categories. As such, a conjecture of the second author would imply that images of the braid…
The complex representation rings of finite groups are the fundamental class of fusion rings, categorified by the corresponding fusion categories of complex representations. The category of $\mathbb{Z}_+$-modules of finite rank over such a…
In this paper we study indecomposable rank 2 modules in the Grassmannian cluster category ${\rm CM}(B_{5,10})$. This is the smallest wild case containing modules whose profile layers are $5$-interlacing. We construct all rank 2…
We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…
We investigate tensor products of matrix factorisations. This is most naturally done by formulating matrix factorisations in terms of bimodules instead of modules. If the underlying ring is C[x_1,...,x_N] we show that bimodule matrix…
In this article, we study the classification of some natural numbers related to the combinatorics of congruence subgroups of the modular group. More precisely, we will focus here on the notion of minimal monomial solutions. These are the…
We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank. Our technical advance is a generalization of the Cauchy theorem in group theory to the…
The main goal of this paper is to classify $\ast$-module categories for the $SO(3)_{2m}$ modular tensor category. This is done by classifying $SO(3)_{2m}$ nimrep graphs and cell systems, and in the process we also classify the $SO(3)$…
Given an abelian $p$-group $G$ of rank $n$, we construct an action of the torus $\mathbb{T}^n$ on the stable module $\infty$-category of $G$-representations over a field of characteristic $p$. The homotopy fixed points are given by the…