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arXiv · 1407.3761

Small Connections are cyclic

Andrea Pulita
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Abstract

The main local invariants of a (one variable) differential module over the complex numbers are given by means of a cyclic basis. In the $p$-adic setting the existence of a cyclic vector is often unknown. We investigate the existence of such a cyclic vector in a Banach algebra. We follow the explicit method of Katz, and we prove the existence of such a cyclic vector under the assumption that the matrix of the derivation is small enough in norm.

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Andrea Pulita. 2014-07-14. Small Connections are cyclic. https://arxiv.org/abs/1407.3761

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