The scheme of connected components of the Néron model of an algebraic torus.
El ABC de la Aritmética.
Trivial points on towers of curves
In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.
Component groups of Néron models via rigid uniformization.
Bielliptic and hyperelliptic modular curves X(N) and the group Aut(X(N))
We determine all modular curves X(N) (with N ≥ 7) that are hyperelliptic or bielliptic. We also give a proof that the automorphism group of X(N) is PSL₂(ℤ/Nℤ), whence it coincides with the normalizer of Γ(N) in PSL₂(ℝ) modulo ±Γ(N).
On symmetric square values of quadratic polynomials
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