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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.AG2000
On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field
Everett W. Howe, Hui June Zhu
We prove that for every field k and every positive integer n, there exists an absolutely simple n-dimensional abelian variety over k. We also prove an asymptotic result for finite…
math.AG1998
Plane quartics with Jacobians isomorphic to a hyperelliptic Jacobian
Everett W. Howe
We show how for every integer n one can explicitly construct n distinct plane quartics and one hyperelliptic curve over the complex numbers all of whose Jacobians are isomorphic to…