Seminar in Algebraic Geometry and Number Theory

Abstract: Let k be an algebraically closed field and G be a reductive k-group with Lie algebra g. When k is of characteristic zero, the exponential map allows one to integrate any nilpotent Lie subalgebra u of g into a smooth connected unipotent subgroup U of G (otherwise stated Lie(U) = u). However, when k is of characteristic p > 0 this map is no longer always well defined, and even when it is, integrating the algebraic structure (namely getting a subgroup structure from the subalgebra) is not always possible. In this talk we address the question of integrating p-nil Lie algebras of g when k is of separably good characteristic. This assumption ensures the existence of the so called Springer isomorphisms, that are G-equivariant isomorphisms of schemes from the scheme of nilpotent elements of g to the scheme of unipotent elements of G.