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# Ariyan Javanpeykar "Arakelov theory and covers of curves"

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Salle 314 (IHP)
### Salle 314

#### IHP

Description

Ariyan Javanpeykar (Universiteit Leiden - Université Paris XI)

Arakelov theory and covers of curves

Let X be a curve over a number field. We study invariants of X such as the Belyi degree and the Faltings height. Our main result is an explicit inequality relating these invariants. As a first application, we deduce a conjecture of Edixhoven-de Jong-Schepers. Secondly, we give an algorithmic application. Finally, we give a Diophantine application: Szpiro's small points conjecture is true for hyperelliptic curves. We finish the talk with a short discussion of Edixhoven's strategy to compute etale cohomology in polynomial time and how the above results fit into this program.

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