论文标题
拓扑动力和nip场
Topological dynamics and NIP fields
论文作者
论文摘要
我们研究了在任意nip field $ k $上的某些代数群体行动的可定义拓扑动态。我们表明，如果$ k $的乘法群体不是类型的连接，则可以找到一种对Ellis组的猜想，尤其是在DP-Minimal Fields的情况下，$ k $的乘法组与$ k $的乘法组无关，尤其是在dp-Minimal Fields的情况下，$ k $ of $ \ mathrm {sl} _2（k）$的通用定义流的ELLIS组是非平凡的。我们还研究了$ k $的代数群体的某些结构理论，该理论具有可确定的f-enerics。
We study definable topological dynamics of some algebraic group actions over an arbitrary NIP field $K$. We show that the Ellis group of the universal definable flow of $\mathrm{SL}_2(K)$ is non-trivial if the multiplicative group of $K$ is not type-definably connected, providing a way to find multiple counterexamples to the Ellis group conjecture, particularly in the case of dp-minimal fields. We also study some structure theory of algebraic groups over $K$ with definable f-generics.
