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arXiv · 2304.00855

On Fontaine's conjecture for torsion crystalline local systems

Yong Suk Moon
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Abstract

Let $\mathfrak{X}$ be a smooth connected $p$-adic formal scheme. Based on the prismatic description of crystalline local systems, we prove an analogue of Fontaine's conjecture for torsion crystalline local systems on the generic fiber of $\mathfrak{X}$. As an application, we show that the locus of crystalline local systems whose Hodge-Tate weights lie in a fixed interval cuts out a closed subscheme of the universal deformation ring.

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Yong Suk Moon. 2023-04-03. On Fontaine's conjecture for torsion crystalline local systems. https://arxiv.org/abs/2304.00855

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