Related papers: Modular unit and cuspidal divisor class groups of …

We consider the generalized Jacobian $\widetilde{J}$ of the modular curve $X_0(N)$ of level $N$ with respect to a reduced divisor consisting of all cusps. Supposing $N$ is square free, we explicitly determine the structure of the…

We study the real components of modular curves. Our main result is an abstract group-theoretic description of the real components of a modular curve defined by a congruence subgroup of level N in terms of the corresponding subgroup of…

We consider the cones of curves and divisors on the moduli space of stable pointed rational curves,M_n, and on the quotient by the symmetric group, Q_n, which is a moduli space of pairs. We find generators for contractible extremal rays of…

The genus of projective curves discretely separates decidedly different two variable algebraic relations. So, we can focus on the connected moduli M_g of genus g curves. Yet, modern applications require a data variable (function) on such…

For a rational map $\phi: X \to G$ from a normal algebraic variety $X$ to a commutative algebraic group $G$, we define the modulus of $\phi$ as an effective divisor on $X$. We study the properties of the modulus. This work generalizes the…

In this note some new Frobenius type divisibility results are obtained for premodular categories. In particular, we extend Corollary 3.4 of [Yu20] from the settings of super-modular categories to arbitrary pseudo-unitary premodular…

Generalizing work by Pinzari and Roberts, we characterize actions of a compact quantum group G on C*-algebras in terms of what we call weak unitary tensor functors from Rep G into categories of C*-correspondences. We discuss the relation of…

We construct an explicit family of modular iterated integrals which involves cusp forms. This leads to a new method of producing "invariant versions" of iterated integrals of modular forms. The construction will be based on an extension of…

Given a finite modular tensor category, we associate with each compact surface with boundary a cochain complex in such a way that the mapping class group of the surface acts projectively on its cohomology groups. In degree zero, this action…

Inspired by the group structure on $S^1/ \bbZ$, we introduce a weak hopfish structure on an irrational rotation algebra $A$ of finite Fourier series. We consider a class of simple $A$-modules defined by invertible elements, and we compute…

For $N$ integer $\ge1$, K. Murty and D. Ramakrishnan defined the $N$-th Heisenberg curve, as the compactified quotient $X'_N$ of the upper half-plane by a certain non-congruence subgroup of the modular group. They ask whether the…

In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existence part of the conjecture, under a mild adjustment of both…

Let $X$ be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring $R$, and $\mathfrak{m}$ a modulus on $X$, given by a closed subscheme of $X$ which is geometrically reduced. The…

Gives the most precise available description of the p-Frattini module for any p-perfect finite group G=G_0 (Thm. 2.8), and therefore of the groups G_{k,ab}, k \ge 0, from which we form the abelianized M(odular) T(ower). \S 4 includes a…

This paper is devoted to the more elementary aspects of the contramodule story, and can be viewed as an extended introduction to the more technically complicated arXiv:1503.05523. Reduced cotorsion abelian groups form an abelian category,…

We study pullbacks of modular forms of weight 1 from the modular curve X(4) to the modular curve X(4p), where p is an odd prime. We find the extent to which such modular forms separate points on X(4p). Our main result is that these modular…

In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are…

The representation theory of a conformal net is a unitary modular tensor category. It is captured by the bimodule category of the Jones-Wassermann subfactor. In this paper, we construct multi-interval Jones-Wassermann subfactors for unitary…

Let $N$ be a non-squarefree positive integer and let $\ell$ be an odd prime such that $\ell^2$ does not divide $N$. Consider the Hecke ring $\mathbb{T}(N)$ of weight $2$ for $\Gamma_0(N)$, and its rational Eisenstein primes of…

We use ideas from the Strominger--Yau--Zaslow conjecture and microlocal sheaf theory to define graded modules associated with permissible $C^{\infty}$-divisors on compact tropical manifolds. A $C^{\infty}$-divisor is a generalization of a…