Analytic Nullstellensätze and the model theory of valued fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929267897532416 |
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| author | Aschenbrenner, Matthias Srhir, Ahmed |
| author_facet | Aschenbrenner, Matthias Srhir, Ahmed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03979 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Analytic Nullstellensätze and the model theory of valued fields Aschenbrenner, Matthias Srhir, Ahmed Logic Commutative Algebra 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. |
| title | Analytic Nullstellensätze and the model theory of valued fields |
| topic | Logic Commutative Algebra |
| url | https://arxiv.org/abs/2207.03979 |