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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.AG2001
Slope estimates of Artin-Schreier curves
Jasper Scholten, Hui June Zhu
Let f(x) = x^d + a_{d-1}x^{d-1} + ... + a_0 be a polynomial of degree d in Q[x]. For every prime number p coprime to d and f(x) in (Z_p \cap Q)[x], let X/F_p be the Artin-Schreier…
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…