Diophantine Equations in Low Dimensions

Enrico Bombieri

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2000)

  • Volume: 11, Issue: S1, page 11-29
  • ISSN: 1120-6330

Abstract

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This lecture is a survey of recent results in the theory of diophantine equations, especially for dimension 1. The unit equation and its generalizations are examined in detail, as well as Baker's theory and the consequences of the abc-conjecture.

How to cite

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Bombieri, Enrico. "Diophantine Equations in Low Dimensions." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 11.S1 (2000): 11-29. <http://eudml.org/doc/289685>.

@article{Bombieri2000,
abstract = {This lecture is a survey of recent results in the theory of diophantine equations, especially for dimension 1. The unit equation and its generalizations are examined in detail, as well as Baker's theory and the consequences of the abc-conjecture.},
author = {Bombieri, Enrico},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
language = {eng},
month = {12},
number = {S1},
pages = {11-29},
publisher = {Accademia Nazionale dei Lincei},
title = {Diophantine Equations in Low Dimensions},
url = {http://eudml.org/doc/289685},
volume = {11},
year = {2000},
}

TY - JOUR
AU - Bombieri, Enrico
TI - Diophantine Equations in Low Dimensions
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/12//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - S1
SP - 11
EP - 29
AB - This lecture is a survey of recent results in the theory of diophantine equations, especially for dimension 1. The unit equation and its generalizations are examined in detail, as well as Baker's theory and the consequences of the abc-conjecture.
LA - eng
UR - http://eudml.org/doc/289685
ER -

References

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  10. J.- EVERTSE, H. - SCHLICKEWEI, H. P. - SCHMIDT, W.M., Linear equations in variables which lie in a multiplicative group. Annals of Math., submitted. Zbl1026.11038MR1923966DOI10.2307/3062133
  11. FALTINGS, G., Diophantine approximation an Abelian varieties. Annals of Math., 133, 1991, 549-576. Zbl0734.14007MR1109353DOI10.2307/2944319
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