On the number of points on abelian and Jacobian varieties over finite fields
Tom 160 / 2013
Acta Arithmetica 160 (2013), 201-241 MSC: 11G10, 11G20, 11G25, 14G10, 14G15. DOI: 10.4064/aa160-3-1
We give upper and lower bounds for the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian surfaces.