Let $k$ be a field with characteristic $p$. Let $C$ be a projective curve over $k$, which may be disconnected or singular.
What are the (universal?) definitions of the arithmetic genus and the geometric genus of $C$?
Let $k$ be a field with characteristic $p$. Let $C$ be a projective curve over $k$, which may be disconnected or singular.
What are the (universal?) definitions of the arithmetic genus and the geometric genus of $C$?
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