Decomposing Jacobians of curves over finite fields in the absence of algebraic structure

JOURNAL OF NUMBER THEORY

卷:156

Article

Ahmadi, Omran¹  McGuire, Gary²  Rojas-Leon, Antonio³ 

[1] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

[2] Univ Coll Dublin, Sch Math Sci, Dublin 2, Ireland

[3] Univ Seville, Dept Algebra, Seville, Spain

关键词: Curve;    Jacobian;    Supersingular;    Finite field;    L-polynomial;   

DOI  :  10.1016/j.jnt.2015.04.014

来源: Elsevier

【 摘 要 】

We consider the issue of when the L-polynomial of one curve over F-q divides the L-polynomial of another curve. We prove a theorem which shows that divisibility follows from a hypothesis that two curves have the same number of points over infinitely many extensions of a certain type, and one other assumption. We also present an application to a family of curves arising from a conjecture about exponential sums. We make our own conjecture about L-polynomials, and prove that this is equivalent to the exponential sums conjecture. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free