Submission date: 8 July 2022

Abstract:

We present a uniform framework for establishing Nullstellensätze for power series rings using quantifier elimination results for valued fields. As an application we obtain Nullstellensätze for p-adic power series (both formal and convergent) analogous to Rückert'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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Full text arXiv 2207.03979: pdf, ps.