PreprintCC BY 4.0arXiv
From Cell Decomposition to Motivic Integration, Hensel Minimality, and Point Counting
Abstract
Following Macintyre's quantifier elimination result for semi-algebraic p-adic sets from 1976, Denef's cell decomposition from 1984 has played a catalyzing role for both motivic integration and Hensel minimality. Motivic integration has in turn been applied in the Langlands program via transfer principles to change the characteristic of the local field, e.g., for the fundamental lemma. Hensel minimality has been used to study rational points on definable sets, providing non-archimedean analogues of results by Pila and Wilkie in o-minimal structures. I will review some related results and open questions.
Versions
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BibTeX
@misc{cluckers2026from,
title = {{From Cell Decomposition to Motivic Integration, Hensel Minimality, and Point Counting}},
author = {Raf Cluckers},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09852},
eprint = {2610.09852},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09852},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - From Cell Decomposition to Motivic Integration, Hensel Minimality, and Point Counting
AU - Raf Cluckers
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09852
UR - https://arxiv.org/abs/2610.09852
AB - Following Macintyre's quantifier elimination result for semi-algebraic p-adic sets from 1976, Denef's cell decomposition from 1984 has played a catalyzing role for both motivic integration and Hensel minimality. Motivic integration has in turn been applied in the Langlands program via transfer principles to change the characteristic of the local field, e.g., for the fundamental lemma. Hensel minimality has been used to study rational points on definable sets, providing non-archimedean analogues of results by Pila and Wilkie in o-minimal structures. I will review some related results and open questions.
ER -