论文标题
分析无效的零星和有价值领域的模型理论
Analytic Nullstellensätze and the model theory of valued fields
论文作者
论文摘要
我们提出了一个统一的框架，用于使用有价值场的量化器消除结果来建立功率序列环的无效环。作为一个应用程序，我们以$ P $ ADIC Power Series（正式和收敛性）的价格获得了Nullstellensätze，类似于Rückert的Complex和Risler的真正无效的Nullstellensatz，以及Hilbert的第17个问题的$ P $ - addic分析版。还考虑了限制性功率系列的类似声明，包括真实的和$ p $ - adic。
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.
