Clay Mathematics Institute

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Relative Manin-Mumford and integration in elementary terms

David Masser (Mathematisches Institut Basel)

Abstract: Recently with Umberto Zannier we have shown that an algebraic curve in an abelian scheme with relative dimension at least two meets the torsion in at most finitely many points unless there is a good reason not to (and provided everything is defined over the algebraic numbers). This can be applied to Pell's Equation over polynomial rings and the integration of parametrized algebraic functions in elementary terms.