Separated Belyi Maps
نویسندگان
چکیده
We construct Belyi maps having specified behavior at finitely many points. Specifically, for any curve C defined over Q, and any disjoint finite subsets S, T ⊂ C(Q), we construct a finite morphism φ : C → P such that φ ramifies at each point in S, the branch locus of φ is {0, 1,∞}, and φ(T ) ∩ {0, 1,∞} = ∅. This refines a result of Mochizuki’s. We also prove an analogous result over fields of positive characteristic, and in addition we analyze how many different Belyi maps φ are required to imply the above conclusion for a single C and S and all sets T ⊂ C(Q) \ S of prescribed cardinality.
منابع مشابه
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تاریخ انتشار 2013