(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.
By Arthur Forey
By Sylvy Anscombe
By Raf Cluckers
By Pablo Cubides Kovacsics
By Lothar Sebastian Krapp
By Michal Szachniewicz
By Ya'acov Peterzil
By Mariana Vicaria
By Matthias Aschenbrenner
By Philip Dittmann
By Adele Padgett
By Juan Camilo Arosemena Serrato
By Pieter Spaas
By Victor Kleptsyn
By Joaquin Brum
By Juan Camilo Arosemena Serrato
By Francesca Arici
By Shirly Geffen
By Amine Marrakchi
By Pieter Spaas
