Corpus ID: 211068919

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

  title={A counterexample to an optimistic guess about \'etale local systems},
  author={Brian Lawrence and Shizhang Li},
  • Brian Lawrence, Shizhang Li
  • Published 2020
  • Mathematics
  • 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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