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Corrigendum: ‘On certain algebraic curves related to polynomial maps, Compositio Math. 103 (1996), 319–350’
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- Journal:
- Compositio Mathematica / Volume 147 / Issue 1 / January 2011
- Published online by Cambridge University Press:
- 18 June 2010, pp. 332-334
- Print publication:
- January 2011
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An argument is given to fill a gap in a proof in the author’s article On certain algebraic curves related to polynomial maps, Compositio Math. 103 (1996), 319–350, that the polynomial Φn(x,c), whose roots are the periodic points of period n of a certain polynomial map x→f(x,c), is absolutely irreducible over the finite field of p elements, provided that f(x,1) has distinct roots and that the multipliers of the orbits of period n are also distinct over
. Assuming that Φn(x,c) is reducible in characteristic p, we show that Hensel’s lemma and Laurent series expansions of the roots can be used to obtain a factorization of Φn(x,c) in characteristic 0, contradicting the absolute irreducibility of this polynomial over the rational field.
. Assuming that Φ