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A Non-Archimedean Approach to Stratifications

2023/11/28 by Immanuel Halupczok, Halupczok, Immanuel
Mathematics · #03C98 #03H05 #12J25 #14B05 #14B20 #32S60 #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2311.16987

openalex publication_date 2023/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These are notes from a mini-course about the main results of arXiv:2206.03438: I explain how, using suitable valued fields, one obtains a natural notion of canonical stratifications (of e.g. algebraic subsets of ℝn). I also explain how the same techniques yield more invariants of singularities, and I present an application to Poincaré series. While some rudimentary knowledge of model theory is useful, the notes should also be accessible without such knowledge. In particular, they contain an introduction to the non-standard analysis needed for this approach.

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