Resumen de Exponentiation of commuting nilpotent varieties

Paul Sobaje

• Let Hbe a linear algebraic group over an algebraically closed field of characteristic p >0. We prove that any “exponential map” for Hinduces a bijection between the variety of r-tuples of commuting [p]-nilpotent elements in Lie(H)and the variety of height rinfinitesimal one-parameter subgroups of H. In particular, we show that for a connected reductive group Gin pretty good characteristic, there is a canonical exponential map for Gand hence a canonical bijection between the aforementioned varieties, answering in this case questions raised both implicitly and explicitly by Suslin, Friedlander, and Bendel.