A note on μ-stabilizers in ACVF
<p>We study <em>µ</em>-stabilizers for groups definable in ACVF in the valued field sort. We prove that Stab<sup><em>µ</em></sup> (<em>p</em>) is an infinite unbounded definable subgroup of <em>G</em> when <em&g...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2022
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| Summary: | <p>We study <em>µ</em>-stabilizers for groups definable in ACVF in the valued field sort. We prove that Stab<sup><em>µ</em></sup> (<em>p</em>) is an infinite unbounded definable subgroup of <em>G</em> when <em>p</em> is standard and unbounded. In the particular case when <em>G</em> is linear algebraic, we show that Stab<sup><em>µ</em></sup> (<em>p</em>) is a solvable algebraic subgroup of <em>G</em>, with dim(Stab<sup><em>µ</em></sup> (<em>p</em>)) = dim(<em>p</em>) when <em>p</em> is <em>µ</em>-reduced and unbounded.</p> |
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