2015/06/09 by Jean-Baptiste Teyssier, Teyssier, Jean-Baptiste
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.1506.02849
arxiv created 2015/06/09 · openalex publication_date 2015/06/09 · arxiv updated 2015/06/10 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The goal of this paper is to motivate a boundedness conjecture on nearby slopes of ℓ-adic sheaves in positive characteristic, and to prove it for smooth curves. For a constructible ℓ-adic sheaf, we prove the finiteness of the set of nearby slopes associated to a given morphism. For the constant sheaf, we prove the vanishing of nearby slopes in case of generalized semi-stable reduction.