• Corpus ID: 232307057

A theorem on meromorphic descent and the specialization of the pro-\'etale fundamental group

  title={A theorem on meromorphic descent and the specialization of the pro-\'etale fundamental group},
  author={Marcin Lara and Jiu Kang Yu and Lei Zhang},
Given a Noetherian formal scheme X̂ over SpfpRq, where R is a complete DVR, we first prove a theorem of meromorphic descent along a possibly infinite cover of X̂. Using this we construct a specialization functor from the category of continuous representations of the pro-étale fundamental group of the special fiber to the category of F -divided sheaves on the generic fiber. This specialization functor partially recovers the specialization functor of the étale fundamental groups. We also express… 
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