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Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.

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Motivation for using etale topology in representability of functors problems

I don't know much about superschemes, but would like to share some viewpoints for representability of functors on ordinary schemes. A theorem of Grothedieck states that a representable functor is a sh …
Taisong Jing's user avatar
11 votes
1 answer
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Motivations to study the cohomology of the moduli space of curves

Could anyone give some interesting motivations to understand the cohomology of $\mathcal{M}_g$? What I know: I have read the various approaches to construct $\mathcal{M}_g$ via orbit spaces for group …