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Semi-stable extensions on arithmetic surfaces

C. Soule
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Abstract

On a given arithmetic surface, inspired by work of Miyaoka, we consider vector bundles which are extensions of a line bundle by another one. We give sufficient conditions for their restriction to the generic fiber to be semi-stable. We then apply the arithmetic analog of Bogomolov inequality in Arakelov theory, and deduce from it a lower bound for some successive minima in the lattice of extension classes between these line bundles.

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C. Soule. 2005-05-04. Semi-stable extensions on arithmetic surfaces. https://arxiv.org/abs/math/0505079

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