Multi-centered Dilatations, Congruent Isomorphisms and Rost Double Deformation Space

We introduce multi-centered dilatations of rings, schemes and algebraic spaces, a basic algebraic concept. Dilatations of schemes endowed with a structure (e.g., monoid, group or Lie algebra) are in favorable cases schemes endowed with the same structure. As applications, we use our new formalism to contribute to the understanding of mono-centered dilatations, to formulate and deduce some multi-centered congruent isomorphisms and to interpret Rost double deformation space as a double-centered dilatation.