Let formula_72 be a variety over an algebraically closed field formula_73, formula_24 an algebraic group, for example formula_75. Recall that a "G"-torsor over formula_72 is an algebraic space formula_77 with an action of formula_24 and a map formula_79, such that locally on formula_72 (in étale topology or fppf topology) formula_81 is a direct product formula_82. A "G"-gerbe over "M" may be defined in a similar way. It is an Artin stack formula_83 with a map formula_84, such that locally on "M" (in étale or fppf topology) formula_81 is a direct product formula_86. Here formula_87 denotes the classifying stack of formula_24, i.e. a quotient formula_89 of a point by a trivial formula_24-action. There is no need to impose the compatibility with the group structure in that case since it is covered by the definition of a stack. The underlying topological spaces of formula_83 and formula_72 are the same, but in formula_83 each point is equipped with a stabilizer group isomorphic to formula_24.