Mathematics > Algebraic Geometry
arXiv:2408.02542 (math)
[Submitted on 5 Aug 2024 (v1), last revised 24 Jun 2026 (this version, v2)]
Abstract:Let $(X,Z)$ be a regular pair of pure codimension $r$ over a base scheme $S$ of characteristic $p$. Under the assumption of resolution of singularities, we prove purity for the tame cohomology with coefficient in the logarithmic de Rham-Witt sheaves $\nu_m(n)$ for the regular pair $(X,Z)$, i.e. the existence of a natural isomorphism \[ Ri^!\nu_{X,m}(n)\cong \nu_{Z,m}(n-r)[-r] \] for all $m,n\geq 0$, where the logarithmic de Rham-Witt sheaves $\nu_{X,m}(n)$ are the Frobenius-fixed elements in the de Rham-Witt sheaves $W_m\Omega^{n}_{X/\mathbb{F}_p}$.
Submission history
From: Amine Koubaa [view email]
[v1]
Mon, 5 Aug 2024 15:15:50 UTC (61 KB)
[v2]
Wed, 24 Jun 2026 11:47:33 UTC (52 KB)
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