Corpus ID: 235458230

The minimal ramification problem for rational function fields over finite fields

@inproceedings{BarySoroker2021TheMR,
  title={The minimal ramification problem for rational function fields over finite fields},
  author={L. Bary-Soroker and A. Entin and Arno Fehm},
  year={2021}
}
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. 

References

SHOWING 1-10 OF 77 REFERENCES
Soc
  • 27(1):68–133,
  • 1992
Soc
  • 89(1):159–165,
  • 2014
Minimal ramification and the inverse Galois problem over the rational function field Fp(t)
  • J. Number Theory 143:62–81,
  • 2014
7.
  • Xuliang Zhao, Weiwei Sun, +6 authors Ruixia Tian
  • Medicine
  • The journal of maternal-fetal & neonatal medicine : the official journal of the European Association of Perinatal Medicine, the Federation of Asia and Oceania Perinatal Societies, the International Society of Perinatal Obstetricians
  • 2020
7。,7q,,,hypo。,,。,7q32.3-qter27.7 Mb。of,(diaphragm)。,7q。.
Möbius cancellation on polynomial sequences and the quadratic Bateman-Horn conjecture over function fields
  • arXiv:2008.09905 [math.NT],
  • 2020
Explicit Hilbert’s irreducibility theorem in function fields
We prove a quantitative version of Hilbert's irreducibility theorem for function fields: If $f(T_1,\ldots, T_n,X)$ is an irreducible polynomial over the field of rational functions over a finiteExpand
Not
  • rnz120,
  • 2019
Monodromy of Hyperplane Sections of Curves and Decomposition Statistics over Finite Fields
For a projective curve $C\subset\mathbf{P}^n$ defined over $\mathbf{F}_q$ we study the statistics of the $\mathbf{F}_q$-structure of a section of $C$ by a random hyperplane defined overExpand
SIEVES AND THE MINIMAL RAMIFICATION PROBLEM
The minimal ramification problem may be considered as a quantitative version of the inverse Galois problem. For a nontrivial finite group $G$, let $m(G)$ be the minimal integer $m$ for which thereExpand
Primitive Monodromy Groups of Rational Functions with One Multiple Pole
Primitive monodromy groups of rational functions P/Q, where Q is a polynomial with no multiple roots and deg P > deg Q+1 are classified. There are 17 families of such functions which are not BelyiExpand
...
1
2
3
4
5
...