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arXiv · 2209.05050

Overconvergence of \'etale $(\varphi,\Gamma)$-modules in families

Gal Porat
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Abstract

We prove a conjecture of Emerton, Gee and Hellmann concerning the overconvergence of \'etale $(\varphi,\Gamma)$-modules in families parametrized by topologically finite type $\mathbb{Z}_{p}$-algebras. As a consequence, we deduce the existence of a natural map from the rigid fiber of the Emerton-Gee stack to the rigid analytic stack of $(\varphi,\Gamma)$-modules.

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Gal Porat. 2022-09-12. Overconvergence of \'etale $(\varphi,\Gamma)$-modules in families. https://arxiv.org/abs/2209.05050

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