Lie invariant Frobenius lifts on linear algebraic groups

2018/08/03 by Alexandru Buium, Buium, Alexandru
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1808.01289

arxiv created 2018/08/03 · openalex publication_date 2018/08/03 · arxiv updated 2018/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if G is a linear algebraic group over a number field and if G is not a torus then for all but finitely many primes p the p-adic completion of G does not possess a Frobenius lift that is "Lie invariant mod p" (in the sense of \citealie1). This is in contrast with the situation of elliptic curves studied in \citealie1.

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