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arXiv · 2510.26984

Minima successifs des r\'eseaux et pentes des fibr\'es vectoriels sur les corps de fonctions globaux

Jean-Benoît Bost·Frédéric Paulin
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Abstract

Let ${\bf C}$ be a smooth geometrically connected projective curve over a finite field, and let $A$ be the affine algebra of its regular functions outside a fixed place of ${\bf C}$. We give precise relationships between the Mahler successive minima of normed $A$-lattices and the Harder-Narasimhan slopes of vector bundles over ${\bf C}$ using their category equivalence.

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Jean-Benoît Bost, Frédéric Paulin. 2025-10-30. Minima successifs des r\'eseaux et pentes des fibr\'es vectoriels sur les corps de fonctions globaux. https://arxiv.org/abs/2510.26984

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