PetscheClaytonMathematicsCriticallySeparableRational(AM).pdf

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Citeable URL: https://ir.library.oregonstate.edu/concern/defaults/ft848r10n

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Attribute Name	Values
Creator	Petsche, Clayton
Abstract	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 for elliptic curves. We also define the minimal critical discriminant, a global object which can be viewed as a measure of arithmetic complexity of a rational map. We formulate a conjectural bound on the minimal critical discriminant, which is analogous to Szpiro’s conjecture for elliptic curves, and we prove that a special case of our conjecture implies Szpiro’s conjecture in the semistable case.
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	PetscheClaytonMathematicsCriticallySeparableRational_AM_.pdf	2017-07-08	Öffentlich	Herunterladen