F-divided bundles on normal F-finite schemes

2025/10/12 by Langer, Adrian, Zhang, Lei · 1 citation
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.10582

Abstract

In this paper we study F-divided bundles on irreducible Noetherian normal F-finite \mathbbF_p-schemes and we show that their Tannakian category is governed by the behaviour at the generic point. In particular, if U⊂ X is an open subset of a normal variety defined over an algebraically closed field then the corresponding homomorphism of F-divided fundamental groups is faithfully flat. This is analogous to a known fact about the topological fundamental group of an open subset of a normal complex analytic variety. We use this result to show that simply connected, proper, normal varieties in positive characteristic admit no nontrivial F-divided bundles. This generalizes an earlier result of H. Esnault and V. Mehta concerning smooth projective varieties, and settles Gieseker's conjecture in a more general setting.

Citations

• Relative Inverse Limit Perfection of Derived Commutative Rings
• Projectivity of the Witt vector affine Grassmannian
• Mapping stacks and categorical notions of properness
• Regular singular stratified bundles and tame ramification
• The Nori fundamental gerbe of a fibered category
• The Elementary Theory of the Frobenius Automorphisms

Cited by

• Relative Gieseker's problem on F-divided bundles

Related

• Relative Gieseker's problem on F-divided bundles
• Vector bundles trivialized by proper morphisms and the fundamental group scheme, II
• Fundamental group schemes of globally F-regular varieties
• Fundamental group-scheme of some rationally connected fibrations
• The étale fundamental group and F-divided sheaves in characteristic p>0