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arXiv · 1704.07574

A homotopy exact sequence for overconvergent isocrystals

Christopher Lazda·Ambrus Pál
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Abstract

In this article we prove exactness of the homotopy sequence of overconvergent $p$-adic fundamental groups for a smooth and projective morphism in characteristic $p$. We do so by first proving a corresponding result for rigid analytic varieties in characteristic $0$, following dos Santos in the algebraic case. In characteristic $p$, we then proceed by a series of reductions to the case of a liftable family of curves, where we can apply the rigid analytic result.

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Christopher Lazda, Ambrus Pál. 2017-04-25. A homotopy exact sequence for overconvergent isocrystals. https://doi.org/10.1017/fms.2021.63

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