Stefan Bara'nczuk

activity

20242026

collaborators

5 papers

math.AG2026

Iterated Cartier Flux and Non-Finite Generation of Tame Polynomial Automorphism Groups over Finite Fields

Stefan Barańczuk, Tomasz Ślusarski

Let $k = F_{q}$ be a finite field of characteristic $p$ , and let \[ U_n(k)=\{F\in\operatorname{TA}_n(k):F(0)=0,\ JF(0)=I_n\}. \] We prove that every special tame polynomial aut…

math.NT2026

Polynomial representatives of finite-field maps: a sharp dimensional dichotomy

Stefan Barańczuk, Tomasz Ślusarski

Let $k = F_{q}$ . A polynomial representative of a finite-set map is a tuple of polynomials inducing that map on the rational-point grid. We prove a sharp distinction between a…

math.AG2026

Prescribed extension spectra of mock automorphisms over finite fields

Stefan BaraÅczuk, Tomasz Ålusarski

We classify the finite-extension permutation spectra occurring in an explicit family of mock automorphisms over finite fields. Every finite nonempty divisor-closed subset of $\N_{>…

math.NT2025

Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve

Stefan BaraÅczuk, Bartosz NaskrÄcki, Matteo Verzobio

Let $A$ be an abelian variety defined over a number field $K$ , $E / K$ be an elliptic curve, and $I ¨ : A \to E^{m}$ be an isogeny defined over $K$ . Let $P \in A (K)$ be such that $Ï(P)=(Q_…

math.NT2024

Hasse-Minkowski theorem for quadratic forms on groups

Stefan BaraÅczuk

Consider groups such as Mordell-Weil groups of abelian varieties over number fields, odd algebraic $K$ -theory groups of number fields, or finitely generated subgroups of the multip…