Semisimple groups interpretable in various valued fields
We study infinite groups interpretable in power bounded T-convex, V-minimal or p-adically closed fields. We show that if G is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups) then, up to a finite index subgroup, it is definably isogenous to a gro...
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| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425100844/type/journal_article |
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| Summary: | We study infinite groups interpretable in power bounded T-convex, V-minimal or p-adically closed fields. We show that if G is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups) then, up to a finite index subgroup, it is definably isogenous to a group
$G_1\times G_2$
, where
$G_1$
is a K-linear group and
$G_2$
is a
$\mathbf {k}$
-linear group. The analysis is carried out by studying the interaction of G with four distinguished sorts: the valued field K, the residue field
$\mathbf {k}$
, the value group
$\Gamma $
, and the closed
$0$
-balls
$K/\mathcal {O}$
. |
|---|---|
| ISSN: | 2050-5094 |