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  • 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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  • description.provenance : Submitted by Deanne Bruner (deanne.bruner@oregonstate.edu) on 2013-03-29T21:49:16Z No. of bitstreams: 2 PetscheClaytonMathematicsCriticallySeparableRational(VOR).pdf: 381161 bytes, checksum: d4b053008abde3d77c3ab1daa21835b3 (MD5) PetscheClaytonMathematicsCriticallySeparableRational(AM).pdf: 240189 bytes, checksum: e69e9aa9462ed0470e8fab29faa41799 (MD5)
  • description.provenance : Approved for entry into archive by Deanne Bruner(deanne.bruner@oregonstate.edu) on 2013-03-29T21:50:07Z (GMT) No. of bitstreams: 2 PetscheClaytonMathematicsCriticallySeparableRational(VOR).pdf: 381161 bytes, checksum: d4b053008abde3d77c3ab1daa21835b3 (MD5) PetscheClaytonMathematicsCriticallySeparableRational(AM).pdf: 240189 bytes, checksum: e69e9aa9462ed0470e8fab29faa41799 (MD5)
  • description.provenance : Made available in DSpace on 2013-03-29T21:50:07Z (GMT). No. of bitstreams: 2 PetscheClaytonMathematicsCriticallySeparableRational(VOR).pdf: 381161 bytes, checksum: d4b053008abde3d77c3ab1daa21835b3 (MD5) PetscheClaytonMathematicsCriticallySeparableRational(AM).pdf: 240189 bytes, checksum: e69e9aa9462ed0470e8fab29faa41799 (MD5) Previous issue date: 2012-11

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