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

Gal Porat

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

Number Theory 2024-06-28 v2

Authors: Gal Porat

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.

Keywords

etale (phi,gamma)-modules overconvergence families emerton-gee stack rigid analytic stack zp-algebras

Cite

@article{arxiv.2209.05050,
  title  = {Overconvergence of \'etale $(\varphi,\Gamma)$-modules in families},
  author = {Gal Porat},
  journal= {arXiv preprint arXiv:2209.05050},
  year   = {2024}
}

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