Stability of Frobenius direct images over surfaces

2014/07/25 by Congjun Liu, Liu, Congjun, Mingshuo Zhou +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.1407.6899

10 pages

arxiv created 2014/07/25 · openalex publication_date 2014/07/25 · arxiv updated 2014/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective surface over an algebraically closed field k of characteristic p> 0 with Ω_X¹ semistable and μ(Ω_X¹)>0. For any semistable (resp. stable) bundle W of rank r, we prove that F_*W is semistable (resp. stable) when p≥ r(r-1)²+1.

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