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Critically Separable Rational Maps in Families Public Deposited

https://ir.library.oregonstate.edu/concern/articles/k930bx56p

The version of record is embargoed until 10-12-2013. The final peer reviewed, accepted manuscript is available without an embargo. The published article is copyrighted by Foundation Compositio Mathematica and published by Cambridge University Press. It can be found at:  http://journals.cambridge.org/action/displayJournal?jid=com.

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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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  • Clayton Petsche (2012). Critically separable rational maps in families. Compositio Mathematica, 148, pp 1880-1896. doi:10.1112/S0010437X12000346.
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  • This research is supported by grant DMS-0901147 of the National Science Foundation.
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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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