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International Conference and Workshop on Valuation Theory
July 26 - August 11, 1999
University of Saskatchewan
Saskatoon, SK, Canada

Organizers
Franz-Viktor Kuhlmann, Salma Kuhlmann, Murray Marshall, Deirdre Haskell, Hans Schoutens

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Quantifier Elimination for the Relative Frobenius
by
Thomas Scanlon
Berkeley

Let (K, v) be a complete discretely valued field of mixed characteristic with an algebraically closed residue field. Equip K with a continuous automorphism \sigma: K --> K lifting the Frobenius in the sense that \sigma(x) \equiv xp (mod mK) for x in OK. The structure (K, v, \sigma) does not admit elimination of quantifiers in the language of valued difference fields, but it does in natural expansions involving additive-multiplicative-congruences or angular component functions.

I plan to explain the meaning of this theorem in detail and sketch a proof based on a reduction to a quantifier elimination theorem for general valued difference and differential field of equicharacteristic zero.

Date received: July 12, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-79.