Lifting iterated Frobenius over W_n(k)

2019/09/19 by Yukihide Takayama, Takayama, Yukihide
Mathematics · #14B10 #14G17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1909.08900

openalex publication_date 2019/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth scheme over a perfect field k of positive characteristic. M.V.~Nori and V.~Srinivas studied infinitesimal liftings of Frobenius morphism F:X→ X. Namely, given a Frobenius lifting F_Y: Y→ Y over W_n-1(k) the obstruction of lifting F_Y over W_n(k) is a class in H¹(X, T_X\tensor B₁Ω¹_X/k). We give a modified version of their theory and applications, in which we consider lifting (n-1)th iterated Frobenius F^n-1:X→ X directly over W_n(k).

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