Some Historical Notes

Gerd Faltings

Chapter Chapter I in Arithmetic Geometry, 1986, pp 1-8 from Springer

Abstract: Abstract The purpose of these notes is to give some information about the origin of the ideas used in the proofs of the conjectures of Tate, Shafarevich, and Mordell. They are not meant to be a complete historical treatment, and they present only the author’s very personal opinion of how things evolved, and who contributed important ideas. He therefore apologizes in advance for the inaccuracies in them, and that he has omitted many who have contributed their share. He does not intend to offend them, and welcomes advice and remarks. Hopefully his remarks will encourage the reader to look into the original papers. The general strategy is to explain when and why the main ideas were invented. In explaining them we use the modern terminology, which usually makes it much easier to state them than it was at the time when they were first used. Of course, this does not mean that we intend to critize those who invented them, which had to state them at a time when the technical means available were much weaker than those we have today.

Keywords: Modulus Space; Rational Point; Finite Field; Function Field; Abelian Variety (search for similar items in EconPapers)
Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-8655-1_1

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DOI: 10.1007/978-1-4613-8655-1_1

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