Wednesday, September 2 2020
15:30 - 16:30

IMSc Webinar

On a conjecture of Bertrand and Villegas

Sinnou David

University of Paris VI, France

A conjecture of Bertrand and Villegas predict the behaviour of the volumes of subgroups of units of a number field. From the number theoretic point of view, this conjecture can be seen as an interpolation between the still open Lehmer problem (rank 1) and estimates for the regulator (maximal rank). From the arithmetic geometric point of view, it can be interpreted as a prediction on the behaviour of the slopes (Harder-Narasimhan) for some classes of hermitian line bundles. We shall describe some partial results towards this conjecture obtained in collaboration with F. Amoroso.

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