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Do automorphisms actually prevent the formation of fine moduli spaces?

I have found similar questions littered throughout this site and math.SE (for example [1], [2], [3],…), but I feel like like most of them usually just say that non-trivial automorphisms prevent the ...
Coherent Sheaf's user avatar
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Two elliptic curves with the same j-invariants

This is an interesting observation of mine when exploring moduli of elliptic curves. Let's fix a base field $k$ and assume that we have two elliptic curves $E$, $E'$ which are isomorphic over $\bar k$...
fe mu's user avatar
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