(joint with Yatir Halevi and Assaf Hasson) We continue our study of interpretable groups in various valued fields (e.g. RCVF, ACVF and $p$-adically closed fields), and show that if $G$ is an interpretable definably semisimple group, namely has no definable infinite normal abelian subgroup, then, up to a finite index subgroup, it is definably isogenous to a $G_1 \times G_2$, where $G 1$ and $G 2$ are $K$-linear and $k$-linear groups, respectively $(K=$ the valued field and $k=$ the residue field). As in our previous works, we analyze the groups via the 4 distinguished sorts: $K, k, \Gamma$ (value group) and $K / \mathcal{O}$ (the closed 0 -balls), and show that the sorts $\Gamma$ and $K / \mathcal{O}$ do not appear when $G$ is definably semisimple.
De Arthur Forey
De Sylvy Anscombe
De Raf Cluckers
De Pablo Cubides Kovacsics
De Lothar Sebastian Krapp
De Michal Szachniewicz
De Ya'acov Peterzil
De Mariana Vicaria
De Matthias Aschenbrenner
De Philip Dittmann
De Adele Padgett
