Galois action on the Neron-Severi group of Dwork surfaces

2018/09/23 by Duan, Lian
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.08693

Abstract

We study the Galois action attached to the Dwrok surfaces X_λ:X₀⁴+X₁⁴+X₂⁴+X₃⁴-4λX₀X₁X₂X₃=0 with parameter λ in a number field F. We show that when X_λ has geometric Picard number 19, its Néron-Severi group NS(X_λ)⊗ ℚ is a direct sum of quadratic characters. We provide two proofs to this conclusion in our article. In particular, the geometrically proof determines the conductor of each of quadratic characters. Our result matches the one in \citeVoight2. With this decomposition, we give another proof to a result of Wan.

Related

• Galois-invariant Néron--Severi ranks of Fermat surfaces over number fields: a Galois module, closed forms, a threshold, and exact tables
• On the Neron-Severi group of surfaces with many lines
• Sixteen points in \ℙ⁴ and the inverse Galois problem for del\n Pezzo surfaces of degree one
• Neron-Severi group preserving lifting of K3 surfaces and applications
• Some surfaces with maximal Picard number