Logarithmic decomposition of connections on a relatively punctured disk
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929312719962112 |
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| author | Tâm, Pham Thanh |
| author_facet | Tâm, Pham Thanh |
| contents | Let $R=C[[t]]$ be the ring of power series over an algebraically closed field $C$ of characteristic zero. We show that each connection on a finite flat $R((x))$-module is the sum of a regular singular connection and a diagonalizable $R((x))$-linear endomorphism when it admits a Turrittin-Levelt-Jordan form over $R((x))$. This decomposition is compatible with the limit of the logarithmic decompositions of the connections obtained by the reduction modulo $t^{k}$ of a given connection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_08857 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Logarithmic decomposition of connections on a relatively punctured disk Tâm, Pham Thanh Algebraic Geometry 12H05, 13H05, 14F10 Let $R=C[[t]]$ be the ring of power series over an algebraically closed field $C$ of characteristic zero. We show that each connection on a finite flat $R((x))$-module is the sum of a regular singular connection and a diagonalizable $R((x))$-linear endomorphism when it admits a Turrittin-Levelt-Jordan form over $R((x))$. This decomposition is compatible with the limit of the logarithmic decompositions of the connections obtained by the reduction modulo $t^{k}$ of a given connection. |
| title | Logarithmic decomposition of connections on a relatively punctured disk |
| topic | Algebraic Geometry 12H05, 13H05, 14F10 |
| url | https://arxiv.org/abs/2208.08857 |