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math.AG2002★ 14 cited
Curves of every genus with many points, II: Asymptotically good families
Noam D. Elkies, Everett W. Howe, Andrew Kresch +3
We resolve a 1983 question of Serre by constructing curves with many points of every genus over every finite field. More precisely, we show that for every prime power q there is a…
math.NT2002
On the nonexistence of certain curves of genus two
Everett W. Howe
We prove that if q is a power of an odd prime then there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (2-2q)x^2 + q^2. Our…