Why is the space of differential forms on a curve (defined on the fraction field of the coordinate ring) a one-dimensional vector space over the function field of the curve? (I am uncomfortable with most elements of field theory such as transcendence basis or separability so please avoid using them in the answer) Also, what is an analogous statement of this in differential geometry?
2026-03-30 20:51:44.1774903904
Vector space of differential forms on a curve
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