Geometric local epsilon factors

2019/02/18 by Quentin Guignard, Guignard, Quentin · 1 citation
Mathematics · #14F20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1902.06523

openalex publication_date 2019/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by the work of Laumon on ε-factors and by Deligne's 1974 letter to Serre, we give an explicit cohomological definition of ε-factors for ℓ-adic Galois representations over henselian discrete valuation fields of positive equicharacteristic p ≠ ℓ, with (not necessarily finite) perfect residue fields. These geometric local ε-factors are completely characterized by an explicit list of purely local properties, such as an induction formula and the compatibility with geometric class field theory in rank 1, and satisfy a product formula for ℓ-adic sheaves on a curve over a perfect field of characteristic p.

Citations

• Good Reduction of Abelian Varieties

Cited by

• Compatible systems of ℓ-adic sheaves

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