On the cohomology of the Ree groups and kernels of exceptional isogenies

Let G be a simple, simply connected algebraic group over an algebraically closed field k of characteristic p>0. σ:G→G surjective endomorphism such that the fixed point set G(σ) is Suzuki or Ree group. Then, let Gσ denote scheme-theoretic kernel σ. Using methods Jantzen and Bendel–Nakano–Pillen, we compute 1-cohomology for Frobenius kernels with coefficients in induced modules, H1(Gσ,H0(λ)), extensions between simple ExtGσ1(L(λ),L(μ)). When type F4, these results are used to improve known bounds identifying modules defining ExtG(σ)1(L(λ),L(μ)) those