Abstract
We study the Galois action attached to the Dwork surfaces Xλ:X04+X14+X24+X34−4λX0X1X2X3=0 with parameter λ in a number field F. We show that when Xλ has geometric Picard number 19, its Néron-Severi group NS(X‾λ)⊗Q is a direct sum of quadratic characters. We provide two proofs of this result in our article. In particular, the geometric proof determines the conductor of each quadratic character. Our result matches with the one in [DKS+18a]. With this decomposition, this leads to a new proof of Wan's result [Wan06].
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