中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人： 叶谨赫 博士（Institut de Mathématiques de Jussieu-Paris Rive Gauche）
题 目：Beautiful pairs revisited
时 间：2022.04.20（星期三），16:00-17:30
地 点：腾讯会议：577 358 377
摘 要：Hrushovski and Loeser used the stably dominated types \hat{V} as a model-theoretic analogue of Berkovich spaces. Part of the novelty in their approach is that they proved the strict pro-definability of such spaces and generalized the notion of definability in such context. For stable theories T, the theory of beautiful pairs of models T is "meaningful" precisely when the set of all (definable) types in T is strict pro-definable, which is the case if and only if T is nfcp. We generalize the notion of beautiful pairs to unstable theories and study them in particular in henselian valued fields. Particularly, we establish Ax-Kochen-Ershov principles for beautiful pairs of henselian valued fields. As an application, we show that the theories of various beautiful pairs of models of ACVF are "meaningful" and infer the strict pro-definability of the corresponding spaces of definable types in ACVF, e.g., the model theoretic analogue of Huber’s adic spaces and the model theoretic Zariski-Riemann spaces. Joint work with Pablo Cubides Kovacsics and Martin Hils.
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