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arXiv · 2506.13543

Bounding crystalline torsion from \'etale torsion

Ofer Gabber·Shizhang Li
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Abstract

In this note, we prove that given a smooth proper family over a $p$-adic ring of integers, one gets a control of its crystalline torsion in terms of its \'{e}tale torsion, the cohomological degree, and the ramification. Our technical core result is a boundedness result concerning annihilator ideals of $u^{\infty}$-torsion in Breuil--Kisin prismatic cohomology, which might be of independent interest.

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Ofer Gabber, Shizhang Li. 2025-06-16. Bounding crystalline torsion from \'etale torsion. https://arxiv.org/abs/2506.13543

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