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We formulate and prove a log-algebraicity theorem for arbitrary rank Drinfeld modules defined over the polynomial ring F_q[theta]. This generalizes results of Anderson for the rank one case. As an application we show that certain special…

Number Theory · Mathematics 2020-07-09 Chieh-Yu Chang , Ahmad El-Guindy , Matthew A. Papanikolas

In this paper, we compute the natural density of rank-$1$ Drinfeld module over $\mathbb{F}_q[T]$ with surjective adelic Galois representation; and the natural density of rank-$2$ Drinfeld modules over $\mathbb{F}_q[T]$ whose…

Number Theory · Mathematics 2024-07-26 Chien-Hua Chen

We study the group of extensions in the category of Drinfeld modules and Anderson's t-modules, and we show in certain cases that this group can itself be given the structure of a t-module. Our main result is a Drinfeld module analogue of…

Algebraic Geometry · Mathematics 2015-06-29 Matthew A. Papanikolas , Niranjan Ramachandran

Injective modules play an important role in characterizing different classes of rings (e.g. Noetherian rings, semisimple rings). Some semirings have no non-zero injective semimodules (e.g. the semiring of non-negative integers). In this…

Rings and Algebras · Mathematics 2019-04-17 Jawad Abuhlail , Rangga Ganzar Noegraha

See q-alg/9710003 for the corrected version of this paper.

Geometric Topology · Mathematics 2015-06-26 Doug Bullock , Charles Frohman , Joanna Kania-Bartoszynska

The purpose of this paper is to suggest the construction and study properties of semi-infinite induction, which relates to semi-infinite cohomology the same way induction relates to homology and coinduction to cohomology. We prove a version…

q-alg · Mathematics 2008-02-03 Alexander A. Voronov

We give a lower bound for the local height of a non-torsion element of a Drinfeld module.

Number Theory · Mathematics 2007-05-23 Dragos Ghioca

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…

Rings and Algebras · Mathematics 2016-09-15 Donald W. Barnes

Lower Bound for the Canonical Height for Drinfeld Modules with Complex Multiplication. Let K be a fi nite extension of Fq(T), let L=K be a Galois extension with Galois group G and let E be the sub eld of L fixed by the center of G. Assume…

Number Theory · Mathematics 2014-08-06 Hugues Bauchère

In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and…

Optimization and Control · Mathematics 2019-11-07 Christine Bachoc , Dion C. Gijswijt , Alexander Schrijver , Frank Vallentin

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.

Algebraic Geometry · Mathematics 2024-08-07 Lei Zhang

This is a note to revisit interesting results of H. Esnault, C. Sabbah, M. Saito and J.-D. Yu on the Kontsevich complexes from the viewpoint of mixed twistor D-modules. We explicitly describe the V-filtration of the mixed twistor D-modules…

Algebraic Geometry · Mathematics 2017-08-21 Takuro Mochizuki

We study modular polynomials classifying cyclic isogenies between Drinfeld modules of arbitrary rank over the ring F_q[T].

Number Theory · Mathematics 2007-05-23 Florian Breuer , Hans-Georg Rück

We study the passage from Drinfeld-A'-modules to Drinfeld-A-modules for a given finite flat inclusion A \subset A'. We show that this defines a morphism from the moduli space of Drinfeld-A'-modules to the moduli space of Drinfeld-A-modules…

Number Theory · Mathematics 2007-05-23 Urs Hartl , Markus Hendler

Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of…

Quantum Algebra · Mathematics 2024-11-01 Gastón Andrés García , Cristian Vay

The aim of this paper is to discuss the notion of Wieferich primes in the context of Drinfeld modules. Our main result is a surprising connection between the proprety of a monic irreducible polynomial $\mathfrak p$ to be Wieferich and the…

Number Theory · Mathematics 2024-12-17 Xavier Caruso , Quentin Gazda , Alexis Lucas

Let $K/k$ be a finite Galois extension of global function fields. Let $E$ be a Drinfeld module over $k$. We state and prove an equivariant refinement of Taelman's analogue of the analytic class number formula for $(E,K/k)$, and derive…

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…

Exactly Solvable and Integrable Systems · Physics 2025-10-21 Timofey Zolkin , Yaroslav Kharkov , Sergei Nagaitsev

Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in recent years they have also found applications in other…

Algebraic Topology · Mathematics 2024-11-04 Steve Oudot

Let $q\geq2$ be a prime power and consider Drinfeld modules of rank 2 over $\mathbb{F}_q[T]$. We prove that there are no points with coordinates being Drinfeld singular moduli, on a family of hyperbolas $XY=\gamma$, where $\gamma$ is a…

Number Theory · Mathematics 2024-04-12 Bruno Anglès , Cécile Armana , Vincent Bosser , Fabien Pazuki