Related papers: On modular forms of characteristic p>0

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium's p-adic differential characters of elliptic curves and of Manin's differential characters of elliptic curves in differential algebra,…

Our aim is to characterize the homogeneous fractional Sobolev-Slobodecki\u{\i} spaces $\mathcal{D}^{s,p} (\mathbb{R}^n)$ and their embeddings, for $s \in (0,1]$ and $p\ge 1$. They are defined as the completion of the set of smooth and…

Let $X$ be a smooth projective and geometrically irreducible curve over the finite field $\mathbb{F}_q$ with $q$ elements and $K$ be its function field. Let $\infty$ be a fixed closed point on $X$ and $A$ be the ring of functions regular…

In this article we study the family of $BMO^p$ spaces, $p \geq 1$, in the general context of metric measure spaces. We give a characterization theorem that allows to describe all possible relations between these spaces considered as sets of…

The purpose of the present work is to describe a dequantization procedure for topological modules over a deformed algebra. We define the characteristic variety of a topological module as the common zeroes of the annihilator of the…

We define a moduli space of stable regular singular parabolic connections of spectral type on smooth projective curves and show the smoothness of the moduli space and give a relative symplectic structure on the moduli space. Moreover, we…

We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…

Perfect quadratic forms give a toroidal compactification of the moduli space of principally polarized abelian g-folds that is Q-factorial and whose ample classes are characterized, over any base. In characteristic zero it has canonical…

Arbitrarily many pairwise inequivalent modular categories can share the same modular data. We exhibit a family of examples that are module categories over twisted Drinfeld doubles of finite groups, and thus in particular integral modular…

In this short note, we derive dimension formulas for spaces of Drinfeld cusp forms corresponding to harmonic cocycles invariant under the group $\mathrm{SL}_2(\mathbb{F}_q[t])$ and with values in absolutely irreducible…

In~\cite{CS04}, Calegari and Stein studied the congruences between classical cusp forms $S_k(\Gamma_0(p))$ of prime level and made several conjectures about them. In~\cite{AB07} (resp., ~\cite{BP11}) the authors proved one of those…

In previous work we proved that, for categories of free finite-dimensional modules over a commutative semiring, linear compact-closed symmetric monoidal structure is a property, rather than a structure. That is, if there is such a…

We extend work of Voight and the second author to compute the log canonical ring of a wild stacky curve over a field of characteristic $p > 0$, which allows us to compute rings of mod $p$ modular forms of level $\Gamma_{0}(N)$. Our approach…

In this note we show that certain meromorphic orthogonal modular forms are magnetic, i.e.\ their Fourier coefficients satisfy special divisibility criteria. These meromorphic orthogonal modular forms are counterparts to the orthogonal cusp…

We introduce an automorphism $\mathcal{S}$ of the space $C(\mathbb{Z}_p,\mathbb{C}_p)$ of continuous functions $\mathbb{Z}_p \rightarrow \mathbb{C}_p$ and show that it can be used to give an alternative construction of the $p$-adic…

We define complete stable pairs on a smooth projective variety, and construct their moduli space. These moduli spaces have natural morphisms to the moduli of stable pairs and Quot-schemes. As an example, we show that the moduli of complete…

Just as a symmetric surface with separating fixed locus halves into two oriented bordered surfaces, an arbitrary symmetric surface halves into two oriented symmetric half-surfaces, i.e. surfaces with crosscaps. Motivated in part by the…

This is the third part of a series of articles providing a foundation for the theory of Drinfeld modular forms of arbitrary rank. In the present article we construct and study some examples of Drinfeld modular forms. In particular we define…

In this paper we connect Calder\'on and Zygmund's notion of $L^p$\- -differentiability with some recent characterizations of Sobolev spaces via the asymptotics of non-local functionals due to Bourgain, Brezis, and Mironescu. We show how the…