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arXiv · 2208.08857

Logarithmic decomposition of connections on a relatively punctured disk

Pham Thanh Tâm
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Abstract

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.

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Pham Thanh Tâm. 2024-04-13. Logarithmic decomposition of connections on a relatively punctured disk. https://arxiv.org/abs/2208.08857

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