A characterization of the Artin-Mumford curve

Author(s)

Arakelian, Nazar ^[1] ; Korchmaros, Gabor ^[2]

Affiliation

^[1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, BR-13083859 Campinas, SP - Brazil

^[2] Univ Basilicata, Dipartimento Matemat, I-85100 Potenza - Italy

• Document type: Journal article
• Source: JOURNAL OF NUMBER THEORY; v. 154, p. 278-291, SEP 2015.
• Web of Science Citations: 5

Abstract

Let M be the Artin-Mumford curve over the finite prime field F-p with p > 2. By a result of Valentini and Madan, Aut(Fp) (M) congruent to H with H = (C-p x C-p) x Dp-1 We prove that if X is an algebraic curve of genus g = (p - 1)(2) defined over F-p such that Aut(Fp) (X) contains a subgroup isomorphic to H then X is birationally equivalent over F-p to the Artin Mumford curve M. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 14/03497-6 - Rational points on algebraic curves over finite fields
• Grantee: Nazar Arakelian
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor