Monodromy of double elliptic logarithms
Number Theory
2023-05-16 v1 Algebraic Geometry
Abstract
We determine the relative monodromy group of abelian logarithms with respect to periods in the cases of fibered products of elliptic schemes. This gives rise to a result stronger than a theorem due to Y. Andr\'e and implies in particular the algebraic independence of the logarithm of any non-torsion section and the periods. We then conjecture an analogous result for the general case of an abelian scheme of arbitrary relative dimension. This generalizes a theorem of Corvaja and Zannier which determines the said group in the case of a single elliptic scheme.
Keywords
Cite
@article{arxiv.2305.08748,
title = {Monodromy of double elliptic logarithms},
author = {Francesco Tropeano},
journal= {arXiv preprint arXiv:2305.08748},
year = {2023}
}