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СЕМИНАРЫ |
Семинар «Глобус» (записи с 2011 года)
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On the size of generators of solutions of some Diophantine equations М. Хиндриab a Université Paris VII – Denis Diderot b Лаборатория Понселе Независимого московского университета |
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Аннотация: It has been known since at least Fermat that the set of integral solutions to the equation There is a natural notion of size or height of solutions, so an important and natural question is to estimate the minimal size of a set of generators. The questions can easily be generalized on one hand to the group of units of a number field and, on the other hand, to the group of rational points of an abelian variety over a global field. The answer for the first case is essentially known, though there are important unsettled related questions; the answer for the second case is essentially conjectural. We will discuss what we know, conjecture and give examples where theorems may be proven. This will take us to a journey through some arithmetic geometry, zeta functions etc., i.e. several number theorists favourite toys. |