In Luna’s original paper Slices Étale (1973), he proved the existence of an ‘étale slice’ for linearly reductive algebraic group actions over algebraically closed fields of characteristic 0.
This result is the algebraic analogy of the linearization of proper Lie groupoids and is particularly useful in the study of local structure of good quotient stacks.
In this talk, the speaker will start from the definition of linearly reductive groups. The speaker will sketch the proof of the above result which is currently called the Luna’s slice theorem.
Having time, the speaker will also discuss a generalization of Luna’s slice theorem to algebraic stacks given by Alper, Hall and Rydh in their 2020 paper.
