Arul, Vishal;
Booher, Jeremy;
Groen, Steven;
Howe, Everett;
Li, Wanlin;
Matei, Vlad;
Pries, Rachel;
(2023)
Doubly isogenous genus-2 curves with D₄-action.
Mathematics of Computation
, 93
(345)
pp. 347-381.
10.1090/mcom/3891.
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Abstract
We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C are curves over a finite field K, with K-rational base points P and P , and let D and D be the pullbacks (via the Abel–Jacobi map) of the multiplication-by-2 maps on their Jacobians. We say that (C, P) and (C , P ) are doubly isogenous if Jac(C) and Jac(C ) are isogenous over K and Jac(D) and Jac(D ) are isogenous over K. For curves of genus 2 whose automorphism groups contain the dihedral group of order eight, we show that the number of pairs of doubly isogenous curves is larger than na¨ıve heuristics predict, and we provide an explanation for this phenomenon.
| Type: | Article |
|---|---|
| Title: | Doubly isogenous genus-2 curves with D₄-action |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/mcom/3891 |
| Publisher version: | https://doi.org/10.1090/mcom/3891 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Curve, Jacobian, finite field, zeta function, isogeny, unramified cover, arithmetic statistics, ABELIAN SURFACES, JACOBIANS, REDUCTIONS, FAMILIES, FIELDS |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10182126 |
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