Skip to main content
2 of 2
edited tags
Pete L. Clark
  • 65.4k
  • 12
  • 241
  • 381

tamely branched cover over P^1

k is an algebraically closed field, X is a smooth, connected, projective curve over k. f: X-->P^1 is a finite morphism. Let t be a parameter of P^1, suppose f is etale outside t=0 and t=\infty, and tamely ramified over these two points. Prove that f is a cyclic cover, i.e., K(X)=k(t)[h]/(h^n-ut), u is a unit in field k.

TJCM
  • 1.1k
  • 11
  • 21