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Is there a p-adic mathematical structure that incorporates the advantages of both universal Witt vectors (not p-typical-limited; implementing Frobenius and Verschiebung operations) and permitting rational not just integer exponents of p (formulation originally attributed to Poonen -- sum over rationals of the quantity Teichmuller element times p raised to an ordered sequence of rational numbers -- operating in spherically complete closed p-adic space omega)?

Am I correct that "Poonen's formulation" is limited to p-typical applications, and does not permit Frobenius and Verschiebung mapping? And Witt vectors, even universal Witt vectors -- do not operate in the full complete closed p-adic space omega?

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  • $\begingroup$ Any reference for Poonen's formulation? This sounds like something I ought to know... $\endgroup$ – darij grinberg Nov 27 '15 at 19:11
  • $\begingroup$ Scott Carnahan (8/21/07) comments: "How do we write elements of \Omega_p? The answer quite simple, and is found in Poonen’s undergraduate thesis. The elements are exactly those power series \sum_{r \in \mathbb{Q}} a_r p^r with coefficients given by Teichmüller representatives of \overline{\mathbb{F}}_p, such that the set of exponents with nonzero coefficients forms a well-ordered subset of the rationals." Use this link for full write-up: sbseminar.wordpress.com/2007/08/21/p-adic-fields-for-beginners $\endgroup$ – Robert Paster Nov 28 '15 at 0:26

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