Lecture 2: Torsion values for sections in abelian schemes and the Betti map

Lecture 2: Torsion values for sections in abelian schemes and the Betti map

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Umberto Zannier, Scuola Normale Superiore-Pisa
McDonnell Hall A02

We shall consider further variations in the games, obtaining more general Betti maps. We shall also illustrate some links of the Betti map with several other contexts (Manin's theorem of the kernel, linear differential equations, Pell's equation in polynomials, Belyi maps,  extremal polynomials,  Integration in finite terms, Functional transcendence, Kodaira-Spencer map, ...) and state some theorems, both of existence type and finiteness type (obtained mainly in joint work with David Masser).