Rational functions with given ramification in characteristic p

@article{Osserman2006RationalFW,
  title={Rational functions with given ramification in characteristic p},
  author={Brian Osserman},
  journal={Compositio Mathematica},
  year={2006},
  volume={142},
  pages={433 - 450}
}
Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of rational functions (up to automorphism of the target) on the projective line with ramification to order ei at general points Pi, in the case that all ei are less than the characteristic. Unlike the case of characteristic 0, the answer is not given by Schubert calculus, nor is the number of maps always finite for distinct Pi, even in the tamely ramified… 
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