English

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

Number Theory 2020-02-11 v1

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.

Keywords

Cite

@article{arxiv.2002.03799,
  title  = {A counterexample to an optimistic guess about \'etale local systems},
  author = {Brian Lawrence and Shizhang Li},
  journal= {arXiv preprint arXiv:2002.03799},
  year   = {2020}
}

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R2 v1 2026-06-23T13:36:50.281Z