Rational points on curves

Michael Stoll[1]

  • [1] Mathematisches Institut Universität Bayreuth 95440 Bayreuth, Germany.

Journal de Théorie des Nombres de Bordeaux (2011)

  • Volume: 23, Issue: 1, page 257-277
  • ISSN: 1246-7405

Abstract

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This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009.We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve  C over  ℚ . The focus is on practical aspects of this problem in the case that the genus of  C is at least  2 , and therefore the set of rational points is finite.

How to cite

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Stoll, Michael. "Rational points on curves." Journal de Théorie des Nombres de Bordeaux 23.1 (2011): 257-277. <http://eudml.org/doc/219805>.

@article{Stoll2011,
abstract = {This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009.We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve $C$ over $\mathbb\{Q\}$. The focus is on practical aspects of this problem in the case that the genus of $C$ is at least $2$, and therefore the set of rational points is finite.},
affiliation = {Mathematisches Institut Universität Bayreuth 95440 Bayreuth, Germany.},
author = {Stoll, Michael},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Algebraic curves; rational points; Chabauty method; Jacobian; Mordell-Weil sieve},
language = {eng},
month = {3},
number = {1},
pages = {257-277},
publisher = {Société Arithmétique de Bordeaux},
title = {Rational points on curves},
url = {http://eudml.org/doc/219805},
volume = {23},
year = {2011},
}

TY - JOUR
AU - Stoll, Michael
TI - Rational points on curves
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2011/3//
PB - Société Arithmétique de Bordeaux
VL - 23
IS - 1
SP - 257
EP - 277
AB - This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009.We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve $C$ over $\mathbb{Q}$. The focus is on practical aspects of this problem in the case that the genus of $C$ is at least $2$, and therefore the set of rational points is finite.
LA - eng
KW - Algebraic curves; rational points; Chabauty method; Jacobian; Mordell-Weil sieve
UR - http://eudml.org/doc/219805
ER -

References

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