Connected Components of Hurwitz Schemes and Malle’s Conjecture

  title={Connected Components of Hurwitz Schemes and Malle’s Conjecture},
  author={Seyfi T{\"u}rkelli},
  • Seyfi Türkelli
  • Published 2008
Let Z(X) be the number of degree-d extensions of Fq(t) with bounded discriminant and some specified Galois group. The problem of computing Z(X) can be related to a problem of counting Fq-rational points on certain Hurwitz spaces. Ellenberg and Venkatesh used this idea to develop a heuristic for the asymptotic behavior of Z ′(X), the number of -geometrically connectedextensions, and showed that this agrees with the conjectures of Malle for function fields. We extend Ellenberg-Venkatesh’s… CONTINUE READING

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