Matthieu Romagny: The complexity of flat groupoids

The Keel–Mori theorem (1997) ensures existence of quotients for algebraic groups G acting on schemes X with finite stabilizers. With the aim to obtain finer information on these actions, we introduce an invariant that measures the difference between the groupoid defined on X and the equivalence relation on X whose classes are the fibres of the quotient map. This invariant measures the complexity of this action. In complexity < 2 we obtain results of descent of equivariant objects along \(X\to X/G\) as well as a result on quotients by subgroupoids. This is joint work with Gabriel Zalamansky.