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arXiv · 1401.1765

Some properties of analytic difference fields

Silvain Rideau
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Abstract

We prove field quantifier elimination for valued fields endowed with both an analytic structure and an automorphism that are $σ$-Henselian. From this result we can deduce various Ax-Kochen-Ersov type results with respect to completeness and the NIP property. The main example we are interested in is the field of Witt vectors on the algebraic closure of $\mathbb{F}_{p}$ endowed with its natural analytic structure and the lifting of the Frobenius. It turns out we can give a (reasonable) axiomatization of its first order theory and that this theory is NIP.

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Silvain Rideau. 2015-08-18. Some properties of analytic difference fields. https://doi.org/10.1017/s1474748015000183

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