Heights and measures on analytic spaces. A survey of recent results, and some remarks. (English) Zbl 1279.14027

Chambert-Loir, Antoine

Cluckers, Raf (ed.) et al., Motivic integration and its interactions with model theory and non-archimedean geometry. Vol. II. Cambridge: Cambridge University Press (ISBN 978-1-107-64881-4/pbk). London Mathematical Society Lecture Note Series 384, 1-50 (2011).

Summary: This paper has two goals. The first is to present the construction, due to the author [J. Reine Angew. Math. 595, 215–235 (2006; Zbl 1112.14022)], of measures on non-archimedean analytic varieties associated to metrized line bundles and some of its applications. We take this opportunity to add remarks, examples and mention related results.
For the entire collection see [Zbl 1230.14004].

MSC:

14G22	Rigid analytic geometry
14G40	Arithmetic varieties and schemes; Arakelov theory; heights
11G40	\(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture

Citations:

Zbl 1112.14022