Smooth topology

In algebraic geometry, the smooth topology is a certain Grothendieck topology, which is finer than étale topology. Its main use is to define the cohomology of an algebraic stack with coefficients in, say, the étale sheaf formula_1.
To understand the problem that motivates the notion, consider the classifying stack formula_2 over formula_3. Then formula_4 in the étale topology; i.e., just a point. However, we expect the "correct" cohomology ring of formula_2 to be more like that of formula_6 as the ring should classify line bundles. Thus, the cohomology of formula_2 should be defined using smooth topology for formulae like Behrend's fixed point formula to hold.