Abelian Varieties and the Mordell–Lang Conjecture

نویسنده

  • BARRY MAZUR
چکیده

This is an introductory exposition to background material useful to appreciate various formulations of the Mordell–Lang conjecture (now established by recent spectacular work due to Vojta, Faltings, Hrushovski, Buium, Voloch, and others). It gives an exposition of some of the elementary and standard constructions of algebro-geometric models (rather than model-theoretic ones) with applications (for example, via the method of Chabauty) relevant to Mordell–Lang. The article turns technical at one point (the step in the proof of the Mordell–Lang Conjecture in characteristic zero which passes from number fields to general fields). Two different procedures are sketched for doing this, with more details given than are readily found in the literature. There is also some discussion of issues of effectivity.

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تاریخ انتشار 2001