Minima, pentes et algèbre tensorielle

Details Minima, pentes et algèbre tensorielle Minima, pentes et algèbre tensorielle

2011-09-13

arxiv.org/abs/1109.2812v1

Mathematics

Number Theory

16 pages

Scientific paper

Slopes of an adelic vector bundle exhibit a behaviour akin to successive minima. Comparisons between the two amount to a Siegel lemma. Here we use Zhang's version for absolute minima over the algebraic numbers. We prove a Minkowski-Hlawka theorem in this context. We also study the tensor product of two hermitian bundles bounding both its absolute minimum and maximal slope, thus improving an estimate of Chen. We further include similar inequalities for exterior and symmetric powers, in terms of some lcm of multinomial coefficients.

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