Successive minima and slopes of hermitian vector bundles over number fields. (English) Zbl 1100.14513

Borek, Thomas

J. Number Theory 113, No. 2, 380-388 (2005).

Summary: The purpose of this paper is to clarify the relationship between the successive minima and the slopes of a hermitian vector bundle on the spectrum of the ring of integers of an algebraic number field. The main result is a lower and an upper bound for each successive minimum in terms of the corresponding slope.

MSC:

14G40	Arithmetic varieties and schemes; Arakelov theory; heights
14G25	Global ground fields in algebraic geometry
14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)

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