Galois orbits of torsion points near atoral sets
| Autor: | Dimitrov, Vesselin, Habegger, Philipp |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Alg. Number Th. 18 (2024) 1945-2001 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/ant.2024.18.1945 |
| Popis: | We prove that the Galois equidistribution of torsion points of the algebraic torus $\mathbb{G}_{m}^d$ extends to the singular test functions of the form $\log{|P|}$, where $P$ is a Laurent polynomial having algebraic coefficients that vanishes on the unit real $d$-torus in a set whose Zariski closure in $\mathbb{G}_m^d$ has codimension at least $2$. Our result includes a power saving quantitative estimate of the decay rate of the equidistribution. It refines an ergodic theorem of Lind, Schmidt, and Verbitskiy, of which it also supplies a purely Diophantine proof. As an application, we confirm Ih's integrality finiteness conjecture on torsion points for a class of atoral divisors of $\mathbb{G}_m^d$. Comment: New reference, fixed Lemma A.3(i), various minor changes |
| Databáze: | arXiv |
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