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arXiv · 2207.03979

Analytic Nullstellens\"atze and the model theory of valued fields

Matthias Aschenbrenner·Ahmed Srhir
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Abstract

We present a uniform framework for establishing Nullstellens\"atze for power series rings using quantifier elimination results for valued fields. As an application we obtain Nullstellens\"atze for $p$-adic power series (both formal and convergent) analogous to R\"uckert's complex and Risler's real Nullstellensatz, as well as a $p$-adic analytic version of Hilbert's 17th Problem. Analogous statements for restricted power series, both real and $p$-adic, are also considered.

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Matthias Aschenbrenner, Ahmed Srhir. 2022-07-08. Analytic Nullstellens\"atze and the model theory of valued fields. https://arxiv.org/abs/2207.03979

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