Related papers: A Dirichlet unit theorem for Drinfeld modules

We give an explicit formula for the correspondence between simple Yetter-Drinfeld modules for certain finite-dimensional pointed Hopf algebras $H$ and those for cocycle twists $H^{\sigma}$ of $H$. This implies an equivalence between modules…

We study certain modules over the algebra of a Cartier divisor on a scheme. Using these modules, we present an inductive method for studying finite generation properties of algebras and modules. In the context of the minimal model program,…

A method of constructing (finitely generated and projective) right module structure on a finitely generated projective left module over an algebra is presented. This leads to a construction of a first order differential calculus on such a…

Drinfeld's lemma is a powerful tool for splitting $\ell$-adic local systems defined over a product of connected schemes over a finite field. In this paper, we show that Drinfeld's lemma also holds true for algebraic stacks.

In this paper, we study the Galois representations attached to products of Drinfeld modules. As an analogue of Serre's classical result on the images of Galois representations associated with products of elliptic curves, we prove that for…

Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional…

On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends…

The idea of generating integrals analogous to generating functions is first introduced in this paper. A new proof of the well-known Finite Harmonic Series Theorem in Analysis and Analytical Number Theory is then obtained by the method of…

The aim of this paper is to obtain a uniform bound for a certain class of submodules from the following theorem: Let $(R,\frak m)$ be a local ring, let $M$ be a finite $R$--module of dimension $d\ge 1$ and let $\frak q$ be an ideal of $R$…

In this paper, we introduce a Carlitz module analogue of Mersenne primes, and prove Carlitz module analogues of several classical results concerning Mersenne primes. In contrast to the classical case, we can show that there are infinitely…

We show that a pointwise finite-dimensional persistence module indexed over a small category decomposes into a direct sum of indecomposables with local endomorphism rings. As an application of this result we give new, short proofs of…

Let X be a product of Drinfeld modular curves over a general base ring A of odd characteristic. We classify those subvarieties of X which contain a Zariski-dense set of CM points. This is an analogue of the Andr\'e-Oort conjecture. As an…

We prove a Lefschetz theorem for the Tannakian group scheme of $\mathcal{D}$-modules, in arbitrary characteristic. In characteristic $0$, We prove a K\"unneth formula for the Tannakian group scheme of regular singular integrable…

A theory of quasi modules at infinity for (weak) quantum vertex algebras including vertex algebras was previously developed in \cite{li-infinity}. In this current paper, quasi modules at infinity for vertex algebras are revisited. Among the…

The principle "Every result in classical homological algebra should have a counterpart in Gorenstein homological algebra" is given in [3]. There is a remarkable body of evidence supporting this claim (cf. [2] and [3]). Perhaps one of the…

We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.

We prove Dirichlet's theorem for polynomial rings: Let F be a pseudo algebraically closed field. Then for all relatively prime polynomials a(X), b(X)\in F[X] and for every sufficiently large positive integer n there exist infinitely many…

The denominator of the Hilbert series of a finitely generated R-module M does not always divide the denominator of the Hilbert series of R. For this reason, we define the universal denominator. The universal denominator of a module M is the…

It is known in the case of the Stieltjes transform that evaluating the integral by expanding the kernel of transformation followed by term by term integration leads to an infinite series of divergent integrals. Moreover, it is known that…

We explore an analogue of the Andr\'e-Oort conjecture for subvarieties of Drinfeld modular varieties. The conjecture states that a subvariety $X$ of a Drinfeld modular variety contains a Zariski-dense set of complex multiplication (CM)…