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arXiv · 2502.11063

Semi-continuity for conductor divisors of étale sheaves

Haoyu Hu·Jean-Baptiste Teyssier
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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 $\ell$-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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Haoyu Hu, Jean-Baptiste Teyssier. 2026-07-31. Semi-continuity for conductor divisors of étale sheaves. https://arxiv.org/abs/2502.11063

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