Doktorkolloquium: Harry Schmidt

Multiplication polynomials and relative Manin-Mumford

For an elliptic curve E its additive extension is an algebraic group G sitting inside an exact sequence of algebraic groups

0→G_a →G→E→0

where Ga is the additive group. The famous Manin-Mumford conjecture, proved by Hindry for such G, states that the intersection of a curve in G with its set of torsion points is finite unless the curve is contained in an algebraic subgroup. We will present a relative version of this theorem for families of additive extensions. Afterwards we will discuss some consequences of this result for classical problems such as Pell’s equation in polynomials and elementary integration.

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