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arXiv · 2609.08287

A Perfectoid Pro-\'Etale Lie Torsor Can Have a Non-Surjective Sen Map

Tian Qiu·Jiahong Yu
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Abstract

We construct a smooth connected rigid analytic curve over $\mathbb C_p$ with an affinoid perfectoid profinite \'etale $\mathbb Z_p^2$-torsor whose geometric Sen morphism is not surjective, thereby disproving Rodr\'\i guez Camargo's conjectured implication from perfectoidness to surjectivity. The construction relies on a pullback theorem showing that perfectoid profinite \'etale towers are preserved under universally injective morphisms of rigid analytic spaces.

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Tian Qiu, Jiahong Yu. 2026-09-08. A Perfectoid Pro-\'Etale Lie Torsor Can Have a Non-Surjective Sen Map. https://arxiv.org/abs/2609.08287

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