Trivial points on towers of curves

Xavier Xarles[1]

  • [1] Departament de Matemàtiques Universitat Autònoma de Barcelona 08193 Bellaterra, Barcelona, Spain

Journal de Théorie des Nombres de Bordeaux (2013)

  • Volume: 25, Issue: 2, page 477-498
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Xarles, Xavier. "Trivial points on towers of curves." Journal de Théorie des Nombres de Bordeaux 25.2 (2013): 477-498. <http://eudml.org/doc/275811>.

@article{Xarles2013,
abstract = {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.},
affiliation = {Departament de Matemàtiques Universitat Autònoma de Barcelona 08193 Bellaterra, Barcelona, Spain},
author = {Xarles, Xavier},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {trivial point; tower; curve; number field; rational point; gonality},
language = {eng},
month = {9},
number = {2},
pages = {477-498},
publisher = {Société Arithmétique de Bordeaux},
title = {Trivial points on towers of curves},
url = {http://eudml.org/doc/275811},
volume = {25},
year = {2013},
}

TY - JOUR
AU - Xarles, Xavier
TI - Trivial points on towers of curves
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2013/9//
PB - Société Arithmétique de Bordeaux
VL - 25
IS - 2
SP - 477
EP - 498
AB - 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.
LA - eng
KW - trivial point; tower; curve; number field; rational point; gonality
UR - http://eudml.org/doc/275811
ER -

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