Analytic lifting of algebraic tori
Let \(G\) be an analytic group over a complete nonarchimedean field \(k\) and let \(\bar G\) be the algebraic group over the residue field \(\bar k\) of \(k\) which is the reduction of \(G\). The author proves that an affine closed subtorus \(\bar T\) of \(\bar G\) can be lifted to a closed affinoid subtorus \(T\) of \(G\) if \(\bar T\) is \(k\)-split and \(G\) is smooth over the valuation ring of \(k\). The proof uses a rigid-analytic shrinking technique to reduce to the case \(\bar G={\bar {\mathbb G}}^ d_ m\times {\bar {\mathbb G}}^ r_ a\).
analytic group over a complete nonarchimedean field
scientific article; zbMATH DE number 3977166
scientific article