Related papers: Categoricity and covering spaces

Modular categories are important algebraic structures in a variety of subjects in mathematics and physics. We provide an explicit, motivated and elementary definition of a modular category over a field of characteristic 0 as an equivalence…

We apply tilting theory over preprojective algebras $Lambda$ to a study of moduli space of $Lambda$-modules. We define the categories of semistable modules and give an equivalence, so-called reflection functors, between them by using…

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such…

We show that the image of the adelic Galois representation attached to a non-CM modular form is open in the adelic points of a suitable algebraic group. We also show a similar result for the adelic Galois representation attached to a finite…

We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of ``open abelian varieties'' which satisfies gluing axioms similar to those of Riemann surfaces, and…

We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain…

For a certain class of vector bundles E on abelian varieties A over local fields containing all line bundles algebraically equivalent to zero we define a canonical representation of the Tate module of A on the fibre of E in the zero…

We study $N$-congruences between quadratic twists of elliptic curves. If $N$ has exactly two distinct prime factors we show that these are parametrised by double covers of certain modular curves. In many, but not all cases, the modular…

We discuss certain representations of GL 2 Fq[T] in equal characteristic and associated vectorial modular forms

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to…

Geometric Quantization links holomorphic geometry with real geometry, a relation that is a prototype for the modern development of mirror symmetry. We show how to use this treatment to construct a special basis in every space of conformal…

This Bachelor's thesis studies Adelman's construction of the universal abelian category of an additive category. It furthermore extends the construction such that it also applies to transformations between additive functors.

This paper computes the Galois group of the Galois cover of the composition of an \'etale double cover of a cyclic $p$-gonal cover for any prime $p$. Moreover a relation between some of its Prym varieties and the Jacobian of a subcover is…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic…

We study the moduli space of meromorphic 1-forms on complex algebraic curves having at most simple poles with fixed nonzero residues. We interpret the Bergman tau function on this moduli space as a section of a line bundle and study its…

We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a $\Theta$-stratification. These results provide a…

In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and…

We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…