Artin Algebraic Superspace

The étale topology of schemes can be extended to the category of Berezin-Kostant-Leites superschemes . To this end we say that a morphism of superschemes is étale if the underlying morphism of schemes X → Y is étale in the ordinary sense; we can then define étale coverings of superschemes . The étale topology of superchemes is then the Grothendieck topology whose coverings are the étale coverings of superschemes .

In this setting, an étale equivalence relation of superschemes is a categorial equivalence relation . Even in the category of schemes , étale equivalence relations may fail to have categorial quotients, but one can embed schemes into a larger category , that of Artin algebraic spaces, in such way that the quotient of an étale equivalence relation of schemes always exist as an algebraic space [2]. Artin algebraic spaces are particular instances of algebraic stacks .

Analogously, in [1] an Artin algebraic superspace is defined as a sheaf on the categoryof...