classifying stack造句

To understand the problem that motivates the notion, consider the classifying stack B \ mathbb { G } _ m over \ operatorname { Spec } \ mathbf { F } _ q.
For general algebraic stacks the etale topology does not have enough open sets : for example, if G is a smooth connected group then the only etale covers of the classifying stack BG are unions of copies of BG, which are not enough to give the right theory of quasicoherent sheaves.
The notion is of fundamental importance in the study of stacks : a stack that arises in nature is often either a quotient stack itself or admits a stratification by quotient stacks ( e . g ., a Deligne Mumford stack . ) A quotient stack is also used to construct other stacks like classifying stacks or toric stacks.
In the above form, base change has been extended by to the situation where " X ", " S ", and " S "'are ( possibly derived ) stacks, provided that the map " f " is a perfect map ( which includes the case that " f " is a quasi-compact, quasi-separated map of schemes, but also includes more general stacks, such as the classifying stack " BG " of an algebraic group in characteristic zero ).
It's difficult to find classifying stack in a sentence. 用classifying stack造句挺难的