Galois theory of quadratic rational functions

@article{Jones2011GaloisTO,
  title={Galois theory of quadratic rational functions},
  author={R. Jones and M. Manes},
  journal={Commentarii Mathematici Helvetici},
  year={2011},
  volume={89},
  pages={173-213}
}
For a number field K with absolute Galois group G_K, we consider the action of G_K on the infinite tree of preimages of a point in K under a degree-two rational function phi, with particular attention to the case when phi commutes with a non-trivial Mobius transfomation. In a sense this is a dynamical systems analogue to the l-adic Galois representation attached to an elliptic curve, with particular attention to the CM case. Using a result about the discriminants of numerators of iterates of… Expand
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References

SHOWING 1-10 OF 25 REFERENCES
Galois theory of iterated endomorphisms
  • 35
  • PDF
The Image of an Arboreal Galois Representation
  • 34
  • PDF
Iterated Galois towers, their associated martingales, and the $p$-adic Mandelbrot set
  • R. Jones
  • Mathematics
  • Compositio Mathematica
  • 2007
  • 25
  • PDF
The density of prime divisors in the arithmetic dynamics of quadratic polynomials
  • 91
  • PDF
Realising wreath products of cyclic groups as Galois groups
  • 27
PRIMITIVE PRIME DIVISORS IN POLYNOMIAL ARITHMETIC DYNAMICS
  • 29
  • PDF
Galois groups over $$cQ$$ of some iterated polynomials
  • 59
Prime factors of dynamical sequences
  • 30
  • PDF
...
1
2
3
...