Francesco Tropeano

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math.NT2024

Relative monodromy of ramified sections on abelian schemes

Paolo Dolce, Francesco Tropeano

Let's fix a complex abelian scheme $A \to S$ of relative dimension $g$ , without fixed part, and having maximal variation in moduli. We show that the relative monodromy grou…

math.NT2024

Monodromy of elliptic logarithms: some topological methods and effective results

Francesco Tropeano

We present some effective approaches in studying the relative monodromy group of elliptic logarithms with respect to periods of elliptic schemes. We provide explicit ways of constr…

math.NT2024

Finite translation orbits on double families of abelian varieties (with an appendix by E. Amerik)

Ekaterina Amerik, Paolo Dolce, Francesco Tropeano

We study two families of $g$ -dimensional abelian varieties, induced by distinct rational maps defined on a common variety $A$ and mapping to two bases $\overlin…