2018/06/15 by Ichiro Shimada, Shimada, Ichiro
Mathematics · #14J28 #14Q10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #math.AG #msc:14J28 #msc:14Q10
paper · pdf · doi:10.48550/arxiv.1806.05787
32 pages. The proofs in Section 6 are simplified. The main results are not changed
openalex publication_date 2018/06/15 · arxiv created 2019/09/11 · arxiv updated 2019/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The elliptic modular surface of level 4 is a complex K3 surface with Picard number 20. This surface has a model over a number field such that its reduction modulo 3 yields a surface isomorphic to the Fermat quartic surface in characteristic 3, which is supersingular. The specialization induces an embedding of the Néron-Severi lattices. Using this embedding, we determine the automorphism group of this K3 surface over a discrete valuation ring of mixed characteristic whose residue field is of characteristic 3. The elliptic modular surface of level 4 has a fixed-point free involution that gives rise to the Enriques surface of type IV in Nikulin-Kondo-Martin's classification of Enriques surfaces with finite automorphism group. We investigate the specialization of this involution to characteristic 3.