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.
@article{RLIN_2000_9_11_S1_11_0, author = {Enrico Bombieri}, title = {Diophantine Equations in Low Dimensions}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni}, volume = {11}, year = {2000}, pages = {11-29}, zbl = {1149.11306}, mrnumber = {1839739}, language = {en}, url = {http://dml.mathdoc.fr/item/RLIN_2000_9_11_S1_11_0} }
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, Tome 11 (2000) pp. 11-29. http://gdmltest.u-ga.fr/item/RLIN_2000_9_11_S1_11_0/
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