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

@inproceedings{Lara2021ATO, 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}, year={2021} }

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…

## One Citation

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## References

SHOWING 1-10 OF 24 REFERENCES

Specialization map between stratified bundles and pro-étale fundamental group

- MathematicsAdvances in Mathematics
- 2018

The pro-\'etale topology for schemes

- Mathematics
- 2013

We give a new definition of the derived category of constructible $\ell$-adic sheaves on a scheme, which is as simple as the geometric intuition behind them. Moreover, we define a refined fundamental…

Homotopy Exact Sequence for the Pro-Étale Fundamental Group

- Mathematics
- 2019

The pro-etale fundamental group of a scheme, introduced by Bhatt and Scholze, generalizes formerly known fundamental groups -- the usual etale fundamental group $\pi_1^{\mathrm{et}}$ defined in SGA1…

Nori's fundamental group over a non-algebraically closed field

- MathematicsANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- 2018

In this note we generalize Nori's definition of the fundamental group scheme from a rational point to an arbitrary base point so that when we take $X$ to be a field $k$ and the point to be…

Submersions and effective descent of etale morphisms

- Mathematics
- 2007

Using the flatification by blow-up result of Raynaud and Gruson, we obtain new results for submersive and subtrusive morphisms. We show that universally subtrusive morphisms, and in particular…

A General Seifert–Van Kampen Theorem for Algebraic Fundamental Groups

- Mathematics
- 2006

A Seifert–Van Kampen theorem describes the fundamental group of a space in terms of the fundamental groups of the constituents of a covering and the configuration of connected components of the…

ALGEBRAIC AND NORI FUNDAMENTAL GERBES

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2017

In this paper we extend the generalized algebraic fundamental group constructed in Esnault and Hogadi, (Trans. Amer. Math. Soc. 364(5) (2012), 2429–2442) to general fibered categories using the…

Frobenius fixed objects of moduli

- Mathematics
- 2020

. Let X be a category ﬁbered in groupoids over a ﬁnite ﬁeld F q , and let k be an algebraically closed ﬁeld containing F q . Denote by φ k : X k Ñ X k the arithmetic Frobenius of X k { k and suppose…

A crystalline incarnation of Berthelot's conjecture and K\"unneth formula for isocrystals

- Mathematics
- 2018

Berthelot’s conjecture predicts that under a proper and smooth morphism of schemes in characteristic
p
p
, the higher direct images of an overconvergent
F
F
-isocrystal are…