Finite group torsors for the qfh topology, by J.F. Jardine

Suppose that S is a Noetherian scheme and that G is a group scheme which is finite and etale over S. This note shows that G-torsors for the qfh topology coincide up to isomorphism with torsors induced up from the etale topology over such schemes S, in the sense that the obvious comparison function between isomorphism classes of torsors is a bijection. This is the non-abelian analogue of a comparison theorem of Voevodsky which identifies etale and qfh cohomology for coefficient sheaves represented by finite etale abelian group schemes. The method of proof is to show that the qfh stack completion of the group scheme G induces a local weak equivalence of classifying simplicial sheaves for the etale topology.

J.F. Jardine <>