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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1308.0859 |
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| _version_ | 1866914907097661440 |
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| author | Poineau, Jérôme Pulita, Andrea |
| author_facet | Poineau, Jérôme Pulita, Andrea |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1308_0859 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | The convergence Newton polygon of a $p$-adic differential equation III : global decompositions Poineau, Jérôme Pulita, Andrea Number Theory 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. |
| title | The convergence Newton polygon of a $p$-adic differential equation III : global decompositions |
| topic | Number Theory |
| url | https://arxiv.org/abs/1308.0859 |