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arXiv · 2610.23516

On the crystalline Artin--Mumford invariant

Margherita Pagano·Domenico Valloni
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Abstract

Let $k$ be an algebraically closed field of characteristic $p>0$ and let $W=W(k)$. We prove that the torsion subgroup of $H^3_{\mathrm{cris}}(X/W)$ is a birational invariant of smooth projective varieties over $k$. The proof combines the action of correspondences on Hodge--Witt cohomology and on the first Nygaard piece of the de Rham--Witt complex.

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Margherita Pagano, Domenico Valloni. 2026-10-16. On the crystalline Artin--Mumford invariant. https://arxiv.org/abs/2610.23516

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