Fixed point stacks under groups of multiplicative type

Matthieu Romagny (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We prove that if a group scheme of multiplicative type acts on an algebraic stack with affine, finitely presented diagonal then the stack of fixed points is algebraic. For this, we extend two theorems of [SGA3.2] on functors of subgroups of multiplicative type, and functors of homomorphisms from a group of multiplicative type.

Domaines: Géométrie algébrique [math.AG]

Matthieu Romagny. Fixed point stacks under groups of multiplicative type. 2021. ⟨hal-03101022⟩