ag.algebraic geometry – Are maximal tori conjugated locally localizable?


To let $ S $ to be and leave a scheme $ G to S $ to be a reductive group scheme. Then $ G $ admits that there is a maximal torus etale-local, and two maximal tori are conjugate etale-local, according to Theorem 3.2.6 and Corollary 3.2.7 in [B. Conrad, Reductuve group schemes] http://math.stanford.edu/~conrad/papers/luminysga3.pdf.

As stated in the book under Proposition 3.1.9 and at the beginning of Chapter 4, the presence of maximum Tori Zariski locally can be achieved (cf. [SGA3, XIV, 3.20]). My question is the following

To let $ T $ and $ T # $ be maximum tori $ G $ over defined $ S $are they conjugated Zariski-local?

In my case, $ T $ is split $ S $, and $ S $ is affine with $ Pic (S) = 0 $,

I would appreciate comments!