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arXiv · 2609.16638

Arc-analytic functions on locally closed semialgebraic sets

Janusz Adamus·Matthew R. Aharonian·Sean Coverdale·Jaden Visscher
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Abstract

We give a generalization of the Kurdyka theory of arc-analytic functions and arc-symmetric sets on Nash manifolds to the setting of arbitrary locally closed semialgebraic sets. In particular, we prove that the ideals of the ring of arc-analytic functions on a locally closed set $S$ satisfy an arc-analytic Nullstellensatz, their zero-sets are precisely the semialgebraic arc-symmetric subsets of $S$, which form the family of closed sets of a Noetherian topology on $S$, and the Krull dimension of the ring is equal to the Euclidean dimension of $S$ and to the Krull dimension of $S$ in that topology.

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Janusz Adamus, Matthew R. Aharonian, Sean Coverdale, Jaden Visscher. 2026-09-15. Arc-analytic functions on locally closed semialgebraic sets. https://arxiv.org/abs/2609.16638

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