Related papers: On nearly holomorphic Drinfeld modular forms for a…

Let $A$ be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal $I \subset A$, Drinfeld defined the notion of structure of level $I$ on a Drinfeld module. We extend this to that…

We construct and study a natural compactification $\overline{M}^r(N)$ of the moduli scheme $M^r(N)$ for rank-$r$ Drinfeld $\F_q[T]$-modules with a structure of level $N \in \F_q[T]$. Namely, $\overline{M}^r(N) = {\rm Proj}\,{\bf Eis}(N)$,…

In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups made up of the classes admitting invariant, respectively…

Consider a Kleinian singularity $ \mathbb{C}^2/\Gamma $, where $ \Gamma $ is a finite subgroup of $ SL_2(\mathbb{C}) $. In this paper, we construct moduli spaces of framed sheaves on a projective Deligne-Mumford stack compactifying the…

In this paper, we investigate the properties of $A$-coherent and $A$-quasi-coherent sheaves within the framework of algebraic geometry over non-algebraically closed fields. We define an $\mathcal{O}_X$-module to be $A$-coherent (resp.…

We consider generalized Haagerup categories such that $1 \oplus X$ admits a $Q$-system for every non-invertible simple object $X$. We show that in such a category, the group of order two invertible objects has size at most four. We describe…

Let $\mathbb{F}_q$ be the field of $q$ elements and let $A=\mathbb{F}_q[t]$ be the polynomial ring over $\mathbb{F}_q$. Let $\mathfrak{n}\in A\setminus \mathbb{F}_q$ be a monic polynomial with a prime factor of degree prime to $q-1$. Let…

Drinfeld recently suggested to replace projective modules by the flat Mittag--Leffler ones in the definition of an infinite dimensional vector bundle on a scheme $X$. Two questions arise: (1) What is the structure of the class $\mathcal D$…

We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some…

It is often stated that the Carlitz module is to the ring of univariate polynomials over a finite field what the multiplicative group is to the ring of integers. This analogy extends to the "rank 2" case, where Drinfeld modules play a role…

We study de Rham character sheaves on a commutative connected algebraic group $G$, defined as multiplicative line bundles with integrable connection. We construct a group algebraic space $G^\flat$ representing their moduli problem on…

Let $p$ be a prime number, $K$ a finite extension of $\mathbb{Q}_p$ and $n$ an integer $\geq 2$. We completely and explicitly describe the global sections $\Omega^\bullet$ of the de Rham complex of the Drinfeld space over $K$ in dimension…

Let $X$ be a complex smooth quasi-projective surface acted upon by a finite group $G$ such that the quotient $X/G$ has singularities only of ADE type. We obtain an explicit expression for the generating series of the Euler characteristics…

In this dissertation we study the Hodge-Witt cohomology of the $d$-dimensional Drinfeld's upper half space $\mathcal{X} \subset \mathbb{P}_k^d$ over a finite field $k$. We consider the natural action of the $k$-rational points $G$ of the…

In this short note we provide a few examples of non-isomorphic arithmetically equivalent global function fields. These examples are obtained via well-known technique of adjoining the torsion points of various Drinfeld Modules to realise the…

The aim of this article is twofold: first, improve the multiplicity estimate obtained by the second author for Drinfeld quasi-modular forms; and then, study the structure of certain algebras of "almost-$A$-quasi-modular forms"

We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the…

In this article, we give an explicit description of the invertible functions on the Drinfeld symmetric space over $K$ a finite extension of $\mathbb{Q}_p$. We identify them with some distribution spaces over the profinite set of…

We prove that homological filling functions over a ring $R$ equipped with the discrete norm are quasi-isometry invariants for all groups of type $\mathrm{FP}_n$. This confirms a conjecture of Bader-Kropholler-Vankov in the case of discrete…

We study the cup product on the Hochschild cohomology of the stack quotient [X/G] of a smooth quasi-projective variety X by a finite group G. More specifically, we construct a G-equivariant sheaf of graded algebras on X whose G-invariant…