Riso-stratifications and a tree invariant

• David Bradley-Williams ^[2] ; Immanuel Halupczok ^[1]
  1. [1] Heinrich Heine University Düsseldorf

     Heinrich Heine University Düsseldorf

     Kreisfreie Stadt Düsseldorf, Alemania

     
  2. [2] Institute of Mathematics, Czech Academy of Sciences, Czech Republic
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01040-x
• Enlaces
  • Texto completo
• Resumen

  • We introduce a new notion of stratification (“riso-stratifications”), which is canonical and which exists in a variety of settings, including different topological fields like C, R and Qp, and also including different o-minimal structures on R. Riso-stratifications are defined directly in terms of a suitable notion of triviality along strata; the key difficulty and main result is that the strata defined in this way are “algebraic in nature”, i.e., definable in the corresponding first-order language. As an example application, we show that local motivic Poincaré series are, in some sense, trivial along the strata of the riso-stratification. Behind the notion of riso-stratification lies a new invariant of singularities, which we call the “riso-tree”, and which captures, in a canonical way, information that was contained in the non-canonical strata of a Lipschitz stratification. On our way to the Poincaré series application, we show, among others, that our notions interact well with motivic integration.

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