A bound on the genus of a curve with Cartier operator of small rank

2017/10/03 by Zijian Zhou, Zhou, Zijian
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1710.01058

openalex publication_date 2017/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ekedahl showed that the genus of a curve in characteristic p>0 with zero Cartier operator is bounded by p(p-1)/2. We show the bound p+p(p-1)/2 in case the rank of the Cartier operator is 1, improving a result of Re.

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