Geodesic
Lipschitz stratifications in power-bounded o-minimal fields
Journal of the European Mathematical Society, Tome 20 (2018) no. 11, pp. 2717-2767.

Voir la notice de l'article provenant de la source EMS Press

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 o-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.
DOI : 10.4171/jems/823
Classification : 03-XX, 32-XX, 58-XX
Mots-clés : Lipschitz stratifications, polynomially bounded fields, power-bounded fields 
@article{JEMS_2018_20_11_a4,
     author = {Immanuel Halupczok and Yimu Yin},
     title = {Lipschitz stratifications in power-bounded $o$-minimal fields},
     journal = {Journal of the European Mathematical Society},
     pages = {2717--2767},
     publisher = {mathdoc},
     volume = {20},
     number = {11},
     year = {2018},
     doi = {10.4171/jems/823},
     url = {https://geodesic-test.mathdoc.fr/articles/10.4171/jems/823/}
}
TY  - JOUR
AU  - Immanuel Halupczok
AU  - Yimu Yin
TI  - Lipschitz stratifications in power-bounded $o$-minimal fields
JO  - Journal of the European Mathematical Society
PY  - 2018
SP  - 2717
EP  - 2767
VL  - 20
IS  - 11
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.4171/jems/823/
DO  - 10.4171/jems/823
ID  - JEMS_2018_20_11_a4
ER  - 
%0 Journal Article
%A Immanuel Halupczok
%A Yimu Yin
%T Lipschitz stratifications in power-bounded $o$-minimal fields
%J Journal of the European Mathematical Society
%D 2018
%P 2717-2767
%V 20
%N 11
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.4171/jems/823/
%R 10.4171/jems/823
%F JEMS_2018_20_11_a4
Immanuel Halupczok; Yimu Yin. Lipschitz stratifications in power-bounded $o$-minimal fields. Journal of the European Mathematical Society, Tome 20 (2018) no. 11, pp. 2717-2767. doi : 10.4171/jems/823. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/823/

Cité par Sources :