Lipschitz stratifications in power-bounded -minimal fields
Immanuel HalupczokHeinrich-Heine-Universität Düsseldorf, Germany
Yimu YinSun Yat-sen University, Guangzhou, China
We propose to grok Lipschitz stratifications from a non-archimedean point of view and thereby show that they exist for closed definable sets in any power-bounded -minimal structure on a real closed field. Unlike the previous approaches in the literature, our method bypasses resolution of singularities andWeierstraß preparation altogether; it transfers the situation to a non-archimedean model, where the quantitative estimates appearing in Lipschitz stratifications are sharpened into valuation-theoretic inequalities. Applied to a uniform family of sets, this approach automatically yields a family of stratifications which satisfy the Lipschitz conditions in a uniform way.
Cite this article
Immanuel Halupczok, Yimu Yin, Lipschitz stratifications in power-bounded -minimal fields. J. Eur. Math. Soc. 20 (2018), no. 11, pp. 2717–2767DOI 10.4171/JEMS/823