The field of definition for dynamical systems on ℙ 1
Compositio Mathematica, Tome 98 (1995) no. 3, pp. 269-304. 
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Silverman, Joseph H. The field of definition for dynamical systems on $\mathbb {P}^1$. Compositio Mathematica, Tome 98 (1995) no. 3, pp. 269-304. http://www.numdam.org/item/CM_1995__98_3_269_0/

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