Semi-continuity for conductor divisors of étale sheaves

2025/02/16 by Haoyu Hu, Hu, Haoyu, Jean-Baptiste Teyssier +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.2502.11063

published as International Mathematics Research Notices, Volume 2026, Issue 3, February 2026, rnag001 · 22 pages. The article has been published in IMRN

arxiv created 2026/07/31 · arxiv updated 2026/08/03

Abstract

In this article, we prove a semi-continuity property for both conductor divisors and logarithmic conductor divisors for étale sheaves on higher relative dimensions in a geometric situation. It generalizes a semi-continuity result for conductors of étale sheaves on relative curves to higher relative dimensions, and it can be considered as a higher dimensional ℓ-adic analogy of André's result on the semi-continuity of Poincaré-Katz ranks of meromorphic connections on smooth relative curves.

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