# Lang's conjecture and level structures on abelian varieties

## Anthony Várilly-Alvarado (Rice University)

Before Mazur proved his theorem on the possible torsion groups on elliptic curves over Q, Manin had shown in 1969 that for a fixed number field K and prime p, the p-primary torsion of elliptic curves over K was uniformly bounded. We will explain a result in this direction for more general abelian varieties, subject to Lang's conjecture on rational points on varieties of general type. This is joint work with Dan Abramovich.

Tuesday, August 23rd, at 4:00pm in HBH 227

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