Article
Decomposing Jacobians of curves over finite fields in the absence of algebraic structure
Author/s | Ahmadi, Omran
McGuire, Gary Rojas León, Antonio |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2015-11 |
Deposit Date | 2016-06-08 |
Published in |
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Abstract | We consider the issue of when the L-polynomial of one curve over Fq 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 ... We consider the issue of when the L-polynomial of one curve over Fq 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. |
Funding agencies | Ministerio de Ciencia e Innovación (MICIN). España European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) |
Project ID. | MTM2010-19298 |
Citation | Ahmadi, O., McGuire, G. y Rojas León, A. (2015). Decomposing Jacobians of curves over finite fields in the absence of algebraic structure. Journal of Number Theory, 156, 414-431. |
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