On continuity of local epsilon factors of ℓ-adic sheaves

2020/03/15 by Daichi Takeuchi, Takeuchi, Daichi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2003.06931

openalex publication_date 2020/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a noetherian scheme and f\colon X→ S be a smooth morphism of relative dimension 1. For a locally constant sheaf on the complement of a divisor in X at over S, Deligne and Laumon proved that the universal local acyclicity is equivalent to the local constancy of Swan conductors. In this article, assuming the universal local acyclicity, we show an analogous result of the continuity of local epsilon factors. We also give a generalization of this result to a family of isolated singularities.

Citations

• Constructible sheaves are holonomic

Related

• Local acyclicity in p-adic cohomology
• Characteristic Epsilon Cycles of ℓ-adic Sheaves on Varieties
• Geometric local ε-factors in higher dimensions
• Geometric local epsilon factors
• Semi-continuity for total dimension divisors of étale sheaves