Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...
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Mathematica 2012.
Criticallyseparablerational maps in families
in K̄, define a rationalmap φa,b,c
Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...
Full Text:
rationalmap φ has exactly 2d− 2
critical points in P1(K̄). We say that φ is criticallyseparable if it has
Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...