p-torsion étale sheaves on the Jacobian of a curve

2019/09/27 by Yifei Zhao, Zhao, Yifei
Mathematics · #11G45 #14H40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1909.12462

openalex publication_date 2019/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose X is a smooth, proper, geometrically connected curve over \mathbb F_q with an \mathbb F_q-rational point x₀. For any \mathbb F_q^×-character σ of π₁(X) trivial on x₀, we construct a functor \mathbb L_n^σ from the derived category of coherent sheaves on the moduli space of deformations of σ over the Witt ring W_n(\mathbb F_q) to the derived category of constructible W_n(\mathbb F_q)-sheaves on the Jacobian of X. The functors \mathbb L_n^σ categorify the Artin reciprocity map for geometric class field theory with p-torsion coefficients. We then give a criterion for the fully faithfulness of (an enhanced version of) \mathbb L_n^σ in terms of the Hasse-Witt matrix of X.

Citations

• Transformation de Fourier generalisee

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