Geodesic
Semisimple groups interpretable in various valued fields
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e127

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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 $K/\mathcal {O}$. 
Halevi, Yatir; Hasson, Assaf; Peterzil, Ya'acov. Semisimple groups interpretable in various valued fields. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e127. doi: 10.1017/fms.2025.10084
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