Forgetful functor

It is clear that it makes S(g, p) into a stack in groupoids over Sch. The forgetful functor of S(g,p) into the stack of principally polarized abelian varieties Ag defines a 1-morphism of stacks... 

Note that there is a natural restriction functor Mod(H (X)) —> Mod(X), which sends Qch(G, X) to Qch(X). This functor is regarded as the forgetful functor, forgetting the G-action. The equivariant duahty theorem which we are going to establish must be compatible with this restriction functor, otherwise the theory would be something different from the usual scheme theory and probably useless. 

This construction defines a functor from the category of liftings to the category of trivialized extensions. It is obviously an equivalence of categories which is quasi-inverse to the functor "forget the structure of extension". 

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