Monodromy of double elliptic logarithms
Francesco Tropeano
Università della Calabria, Rende, Italy
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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. André 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.
Cite this article
Francesco Tropeano, Monodromy of double elliptic logarithms. Rend. Sem. Mat. Univ. Padova (2024), published online first
DOI 10.4171/RSMUP/156