Algebraic-group torsor
= Algebraic-group torsor
{wiki=Principal_bundle}
For an algebraic group $H$, a flat $H$-torsor over $Y$ is a faithfully flat morphism $X\to Y$ with a right $H$-action such that $X\times H\to X\times_YX$, $(x,h)\mapsto(x,xh)$, is an isomorphism. A Zariski torsor additionally becomes $U\times H$ on a Zariski open cover of $Y$.