Abstract
The aim of this course is the study of rational and integral points on algebraic varieties, especially on curves or abelian varieties. Before the end of the last century only special cases had been considered. The first general results are found, around 1890, in the work of Hurwitz and Hilbert [HH] where they introduced the, nowadays natural, viewpoint of algebraic geometry: if X and X′ are two birationally equivalent algebraic curves over Q in P 2 , their rational points correspond. Hence the importance of birational invariants, in particular the genus.
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© 1997 Springer Fachmedien Wiesbaden
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Serre, JP. (1997). Summary. In: Brown, M. (eds) Lectures on the Mordell-Weil Theorem. Aspects of Mathematics, vol 15. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-10632-6_1
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DOI: https://doi.org/10.1007/978-3-663-10632-6_1
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-663-10634-0
Online ISBN: 978-3-663-10632-6
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