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The Elementary Theory of the Frobenius Automorphisms

Abstract:

A Frobenius difference field is an algebraically closed field of characteristic $p>0$, enriched with a symbol for $x \mapsto x^{p^m}$. We study a sentence or formula in the language of fields with a distinguished automorphism, interpreted in Frobenius difference fields with $p$ or $m$ tending to infinity. In particular, a decision procedure is found to determine when a sentence is true in almost every Frobenius difference field. This generalizes Cebotarev's density theorem and Weil's Riema...

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Publication status:
Not published
Peer review status:
Not peer reviewed
Version:
Author's original manuscript

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Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Journal:
arXiv
Publication date:
2004-06-24
Pubs id:
pubs:648761
URN:
uri:f8341253-3d79-4b1b-92e9-7294026decff
UUID:
uuid:f8341253-3d79-4b1b-92e9-7294026decff
Local pid:
pubs:648761

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