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Defining Integrality at Prime Sets of High Density over Function Fields

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Abstract.

 Let F be a function field of characteristic p>2 over a finite field C p . Then for any finite set of F-primes S and any ɛgt;0, there exists a set of F-primes W of density greater than 1-ɛ such that S ⊂W and O F,S has a Diophantine definition over O F,W . (Here O F,W = {x ∈ Fx|ordp x⩾0,∀p∉W} and O F,S is defined analogously.)

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Authors and Affiliations

  1. East Carolina University, Greenville, NC, USA, US

    Alexandra Shlapentokh

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  1. Alexandra Shlapentokh
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Received 5 March 2001; in revised form 4 October 2001

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Shlapentokh, A. Defining Integrality at Prime Sets of High Density over Function Fields. Mh Math 135, 59–67 (2002). https://doi.org/10.1007/s006050200005

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  • DOI: https://doi.org/10.1007/s006050200005

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