Trace and families of algebraic curves.

Gerard van der Geer; M. van der Vlugt

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Trivial points on towers of curves

Xavier Xarles (2013)

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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.