Galois action on the Neron-Severi group of Dwork surfaces

JOURNAL OF NUMBER THEORY

卷:210

Article

Duan, Lian¹ 

[1] Univ Massachusetts, Dept Math & Stat, 710 N Pleast St, Amherst, MA 01003 USA

关键词: Galois representation;    Zeta functions;    Dwork surfaces;    Neron-Severi group;    del Pezzo surfaces;   

DOI  :  10.1016/j.jnt.2019.09.020

来源: Elsevier

【 摘 要 】

We study the Galois action attached to the Dwork surfaces X-lambda : X-0(4) + X-1(4) + X-2(4) + X-3(4) - 4 lambda X0X1X2X3 = 0 with parameter A in a number field F. We show that when X-lambda has geometric Picard number 19, its Neron-Severi group NS((X) over bar (lambda)) circle times 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]. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free