15 citations · 64 across the 25 of their papers we have counts for
26 papers
Algebraic independence of periods of Anderson modules and their hyperderivatives
Andreas Maurischat, Changningphaabi Namoijam
Transcendence questions of periods and quasi-periods of Anderson modules, as well as the hyperderivatives thereof, are of major interest in number theory over function fields. In t…
On purity of Anderson t-modules
Yen-Tsung Chen, Andreas Maurischat
In the theory of abelian Anderson -modules, pure Anderson -modules play an important role. Namoijam and Papanikolas also introduced the notions of strictly pure and almost st…
Determining -motives and dual -motives in Anderson's theory
Andreas Maurischat
Anderson t-modules are analogs of abelian varieties in positive characteristic. Associated to such a t-module, there are its t-motive and its dual t-motive. When dealing with these…
Pairing Anderson motives via formal residues in the Frobenius endomorphism
Quentin Gazda, Andreas Maurischat
Anderson modules form a generalization of Drinfeld modules and are commonly understood as the counterpart of abelian varieties but with function field coefficients. In an attempt t…
Non-abelian Anderson A-modules: Comparison isomorphisms and Galois representations
Andreas Maurischat
In this manuscript, we consider non-abelian Anderson -modules (of generic characteristic). The main results are on the structure of their motives, and on comparison isomorph…
Carlitz twists: their motivic cohomology, regulators, zeta values and polylogarithms
Quentin Gazda, Andreas Maurischat
The integral -motivic cohomology and the class module of a (rigid analytically trivial) Anderson -motive were introduced by the first author in [Gaz22b]. This paper is devote…
Residue of special functions of Anderson -modules at the characteristic graph
Quentin Gazda, Andreas Maurischat
Let be an Anderson -module over . The period lattice of is related to its module of special functions by means of a non-canonical isomorphism introd…
Abelian equals A-finite for Anderson A-modules
Andreas Maurischat
Anderson introduced t-modules as higher dimensional analogs of Drinfeld modules. Attached to such a t-module, there are its t-motive and its dual t-motive. The t-module gets the at…
Algebraic independence of the Carlitz period and its hyperderivatives
Andreas Maurischat
This paper deals with the fundamental period of the Carlitz module. The main theorem states that the Carlitz period and all its hyperderivatives are algebraically indepen…
Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions
Andreas Maurischat, Rudolph Perkins
We generalize our work on Carlitz prime power torsion extension to torsion extensions of Drinfeld modules of arbitrary rank. As in the Carlitz case, we give a description of these…
Anderson t-modules with thin t-adic Galois representations
Andreas Maurischat
Pink has given a qualitative answer to the Mumford-Tate conjecture for Drinfeld modules in the 90s. He showed that the image of the v-adic Galois representation is v-adically open…
Reduced group schemes as iterative differential Galois groups
Andreas Maurischat
This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for…
On field extensions given by periods of Drinfeld modules
Andreas Maurischat
In this short note, we answer a question raised by M. Papikian on a universal upper bound for the degree of the extension of given by adjoining the periods of a Drinfeld…
Special Functions and Gauss-Thakur Sums in Higher Rank and Dimension
Quentin Gazda, Andreas Maurischat
Anderson generating functions have received a growing attention in function field arithmetic in the last years. Despite their introduction by Anderson in the 80s where they were at…
Periods of -modules as special values
Andreas Maurischat
In this article we show that all periods of uniformizable -modules (resp. their coordinates) can be obtained via specializing a rigid analytic trivialization of a related dual $…
Prolongations of t-motives and algebraic independence of periods
Andreas Maurischat
In this article we show that the coordinates of a period lattice generator of the -th tensor power of the Carlitz module are algebraically independent, if is prime to the ch…
An Integral Digit Derivative Basis for Carlitz Prime Power Torsion Extensions
Andreas Maurischat, Rudolph Perkins
Let be a monic irreducible polynomial in , the ring of polynomials in the indeterminate over the finite field , and let be…
A chain rule formula for higher derivations and inverses of polynomial maps
Andreas Maurischat
The multidimensional chain rule formula for analytic functions and its generalisation to higher derivatives perfectly work in the algebraic setting in characteristic zero. In posit…
Non-free iterative differential modules
Andreas Maurischat
In the article "Picard-Vessiot theory of differentially simple rings" we established a Picard-Vessiot theory over differentially simple rings which may not be fields. Differential…
A categorical approach to Picard-Vessiot theory
Andreas Maurischat
Picard-Vessiot rings are present in many settings like differential Galois theory, difference Galois theory and Galois theory of Artinian simple module algebras. In this article we…
Picard-Vessiot theory of differentially simple rings
Andreas Maurischat
In Picard-Vessiot theory, the Galois theory for linear differential equations, the Picard-Vessiot ring plays an important role, since it is the Picard-Vessiot ring which is a torso…
Torsion group schemes as iterative differential Galois groups
Andreas Maurischat
We are considering iterative derivations on the function field L of abelian schemes in positive characteristic p>0, and give conditions when the torsion group schemes of this abeli…
On the finite inverse problem in iterative differential Galois theory
Andreas Maurischat
In positive characteristic, nearly all Picard-Vessiot extensions are inseparable over some intermediate iterative differential extensions. In the Galois correspondence, these inter…
On the finite generation of additive group invariants in positive characteristic
Emilie Dufresne, Andreas Maurischat
Roberts, Freudenburg, and Daigle and Freudenburg have given the smallest counterexamples to Hilbert's fourteenth problem as rings of invariants of algebraic groups. Each is of an a…