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arXiv · 2002.03799

A counterexample to an optimistic guess about \'etale local systems

Brian Lawrence·Shizhang Li
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Abstract

In p-adic Hodge theory, it is known that if a Galois representation is de Rham, then it becomes semistable after extension of the base field. Liu and Zhu asked whether a corresponding result holds in the relative setting: given an \'etale local system on a quasi-compact rigid analytic variety (for example, a projective scheme) over a p-adic field, does it become semistable after a finite extension of the base field? We give a counterexample.

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Brian Lawrence, Shizhang Li. 2020-02-06. A counterexample to an optimistic guess about \'etale local systems. https://arxiv.org/abs/2002.03799

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