A note on $\mu$-stabilizers in ACVF

Abstract

We study $\mu$-stabilizers for groups definable in ACVF in the valued field sort. We prove that ${\mathrm{Stab}}^{\mu }(p)$ is an infinite unbounded definable subgroup of $G$ when $p$ is standard and unbounded. In the particular case when $G$ is linear algebraic, we show that ${\mathrm{Stab}}^{\mu }(p)$ is a solvable algebraic subgroup of $G$, with $\dim ({\mathrm{Stab}}^{\mu }(p))=\dim (p)$ when $p$ is $\mu$-reduced and unbounded.

15 pages

References in corpus (2)

• On non-compact $p$-adic definable groups
• Pro-definability of spaces of definable types