My recent article Essential dimension of algebraic groups, including bad characteristic with Bob Guralnick was named an “Editor’s Choice“. As a consequence, it will be available free open access on the journal website for the next year.
Here’s the abstract: We give upper bounds on the essential dimension of (quasi-) simple algebraic groups over an algebraically closed field that hold in all characteristics. The results depend on showing that certain representations are generically free. In particular, aside from the cases of spin and half-spin groups, we prove that the essential dimension of a simple algebraic group G of rank at least two is at most dim G – 2(rank G) – 1. It is known that the essential dimension of spin and half-spin groups grows exponentially in the rank. In most cases, our bounds are as good as or better than those known in characteristic zero and the proofs are shorter. We also compute the generic stabilizer of an adjoint group on its Lie algebra.