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There are exactly 8 isomorphism classes of curves over finite fields with trivial class group. Of these, 7 were identified by Madan-Queen in 1972 [10.4064/aa-20-4-423-432 , MR:0306160 ]; it was claimed by Leitzel-Madan-Queen in 1975 [0.1016/0022-314X(75)90004-9 , MR:0369326 ] that this list is complete. The 8th example was found by Stirpe in 2014 [10.1016/j.jnt.2014.02.016 , MR:3227356 ], and completeness of the resulting list was proved independently by Mercuri-Stirpe [arXiv:1406.5365 , 10.1016/j.jnt.2015.02.008 , MR:3339577 ] and Shen-Shi [arXiv:1412.3505 , 10.1016/j.jnt.2015.02.005 , MR:3339578 ].

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  • Last edited by Andrew Sutherland on 2019-05-04 20:50:19
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