

Globus Seminar
April 16, 2015 15:40, Moscow, IUM (Bolshoi Vlas'evskii per., 11)






Asymptotic properties of global fields
Ph. Lebacque^{} ^{} Laboratoire de Mathématiques, Université de FrancheComté, Besançon

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Abstract:
Our talk deals with the behaviour of arithmetic data (class number,
number of places of given degree) in families of global fields.
During the first part of our talk, we will motivate this study with
questions related to sphere packings and coding theory. After that,
we will recall the classical Brauer–Siegel theorem that precisely
describes the behaviour of the product of the class number by
the regulator in families, and then give some generalizations and
applications. For this purpose, we will introduce Tsfasman–Vladuts
invariants of infinite global fields.
In the second part of our talk, we will first explain Schmidt"s
$K(pi,1)$ property and make use of it in order to construct nice
families of global fields. Then, if time permits, we will give another
related context where this property plays a major role. Finally,
we will raise some open questions and explain why they are interesting
and difficult.
Доклад будет прочитан на английском языке.

