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math.AG2001
Families of supersingular curves in characteristic 2
Jasper Scholten, Hui June Zhu
This paper determines the normal forms of hyperelliptic supersingular curves of genus g over an algebraically closed field F of characteristic 2 for 0 < g< 9. We also show that eve…
math.AG2000
Hyperelliptic curves in characteristic 2
Jasper Scholten, Hui June Zhu
In this paper we prove that there are no hyperelliptic supersingular curves over F_2bar of genus 2^n-1 for any integer n>1. Let g be a natural number, and h=floor(log_2(g+1)+1). Le…
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…