automorphism groups for p-cyclic covers of the affine line

[摘要] let k be an algebraically closed field of positive characteristic p > 0 and $c o {mathbb p}^1_k$ a p-cyclic cover of the projective line ramified in exactly one point. we are interested in the p-sylow subgroups of the full automorphism group autkc. we prove that for curves c with genus 2 or higher, these groups are exactly the extensions of a p-cyclic group by an elementary abelian p-group. the main tool is an efficient algorithm to compute the p-sylow subgroups of autkc starting from an artin–schreier equation for the cover $c o {mathbb p}^1_k$. we also characterize curves c with genus $g_cgeq 2$ and a p-group action $gsubset ext{aut}_k c$ such that $2p/(p-1)

[学科分类] 数学（综合）