# p adic number theory – conjugation of maximal algebraic tori Accept $$G$$ is a connected, reductive algebraic group over a non-Archimedean local field $$F$$which is divided over a finite extent $$E / F$$,

I often see a result that says "everything is maximum $$F$$-Tori are conjugated over $$E$$", by which I understand the following: Let $$G (E)$$ denote the $$E$$-Dots of the algebraic group $$G$$;; then for each maximum $$F$$-tori $$T, T$$ of $$G$$is there $$x in G (E)$$ so that $$T (E) = xT & # 39; (E) x ^ {- 1}$$,

In addition, the definitions show that if $$T, T$$ are maximum $$F$$-tori from $$G$$then there is an isomorphism of $$T (F)$$ on to $$T & # 39; (F)$$ which is defined via $$E$$,

My question is: Can the isomorphism be assumed to be conjugation in the second statement (as in the first statement)? That means: it follows from these results that if $$T, T$$ are maximum $$F$$-tori in $$G$$then it exists $$x in G (E)$$ so that $$T (F) = xT & # 39; (F) x ^ {- 1}$$?

Any help (including proof of the first statement) is greatly appreciated! Posted on Categories Articles