...but we could have called either one i. That is, complex conjugation (sending i to -i) defines an automorphism C -> C.
I think the mental picture of the two lattices being upside-down from each other is what I was failing to remember
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Also I have an (inaccurate but helpful) picture of the extensions lattice rising in a third dimension from a 2D base field
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I guess C is the prototypical field for me because I always think of them as being flat (which is obviously misleading at times)
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