Dynatomic Galois groups for a family of quadratic rational maps

David Krumm; Allan Lacy

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arXiv · 2303.05632

Dynatomic Galois groups for a family of quadratic rational maps

David Krumm·Allan Lacy

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Abstract

For every nonconstant rational function $\phi\in\mathbb{Q}(x)$, the Galois groups of the dynatomic polynomials of $\phi$ encode various properties of $\phi$ that are of interest in the subject of arithmetic dynamics. We study here the structure of these Galois groups as $\phi$ varies in a particular one-parameter family of maps, namely the quadratic rational maps having a critical point of period 2. In particular, we provide explicit descriptions of the third and fourth dynatomic Galois groups for maps in this family.

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David Krumm, Allan Lacy. 2023-03-10. Dynatomic Galois groups for a family of quadratic rational maps. https://arxiv.org/abs/2303.05632

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