Riso-stratifications and a tree invariant
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00636119" target="_blank" >RIV/67985840:_____/25:00636119 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00029-025-01040-x" target="_blank" >https://doi.org/10.1007/s00029-025-01040-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00029-025-01040-x" target="_blank" >10.1007/s00029-025-01040-x</a>
Alternative languages
Result language
angličtina
Original language name
Riso-stratifications and a tree invariant
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GX20-31529X" target="_blank" >GX20-31529X: Abstract convergence schemes and their complexities</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Selecta Mathematica-New Series
ISSN
1022-1824
e-ISSN
1420-9020
Volume of the periodical
31
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
73
Pages from-to
52
UT code for WoS article
001499216300001
EID of the result in the Scopus database
2-s2.0-105006907701