Finite $p$-subgroups of birational automorphisms and rationality criterion (following J. Xu)

We will prove that the rationally connected variety over algebraically closed field of characteristic zero containing maximally generated $p$-subgroup for $p$ large enough is rational. The proof relies on BABB Fano boundedness theorem, results on $p$-subgroups of birational automorphisms by Yu. Prokhorov and C. Shramov and rationality criterion for a variety with faithful action of split torus, whose statements will be given.