“Separated Belyĭ Maps” by Zachary Scherr and Michael E. Zieve

Zachary Scherr and his graduate advisor Michael E. Zieve have a new paper on the ArXiv entitled “Separated Belyĭ Maps”.

Abstract. We construct Belyĭ maps having specified behavior at finitely many points. Specifically, for any curve C defined over \overline{\mathbb Q}, and any disjoint finite subsets S, T \subset C(\overline{\mathbb Q}), we construct a finite morphism f: C \to \mathbb P^1 such that f ramifies at each point in S, the branch locus of f is \{0,1, \infty \}, and f(T) is disjoint from \{0,1, \infty \}. 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 f are required to imply the above conclusion for a single C and S and all sets T \subset C(\overline{\mathbb Q}) \backslash S of prescribed cardinality.

You can download the paper here.


About Edray Herber Goins, Ph.D.

Edray Herber Goins grew up in South Los Angeles, California. A product of the Los Angeles Unified (LAUSD) public school system, Dr. Goins attended the California Institute of Technology, where he majored in mathematics and physics, and earned his doctorate in mathematics from Stanford University. Dr. Goins is currently an Associate Professor of Mathematics at Purdue University in West Lafayette, Indiana. He works in the field of number theory, as it pertains to the intersection of representation theory and algebraic geometry.
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