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arXiv · 2106.09126

The minimal ramification problem for rational function fields over finite fields

Lior Bary-Soroker·Alexei Entin·Arno Fehm
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Abstract

We study the minimal number of ramified primes in Galois extensions of rational function fields over finite fields with prescribed finite Galois group. In particular, we obtain a general conjecture in analogy with the well studied case of number fields, which we establish for abelian, symmetric and alternating groups in many cases.

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Lior Bary-Soroker, Alexei Entin, Arno Fehm. 2021-06-16. The minimal ramification problem for rational function fields over finite fields. https://arxiv.org/abs/2106.09126

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