The convergence Newton polygon of a $p$-adic differential equation III : global decompositions

Jérôme Poineau; Andrea Pulita

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arXiv · 1308.0859

The convergence Newton polygon of a $p$-adic differential equation III : global decompositions

Jérôme Poineau·Andrea Pulita

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Abstract

We deal with locally free $\mathcal{O}_X$-modules with connection over a Berkovich curve $X$. As a main result we prove local and global decomposition theorems of such objects by the radii of convergence of their solutions. We also derive a bound of the number of edges of the controlling graph, in terms of the geometry of the curve and the rank of the equation. As an application we provide a classification result of such equations over elliptic curves.

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Jérôme Poineau, Andrea Pulita. 2013-08-04. The convergence Newton polygon of a $p$-adic differential equation III : global decompositions. https://arxiv.org/abs/1308.0859

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