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I am a senior studying mathematics at Harvard. I'll start graduate school at Berkeley in the fall.


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comment Existence of divisors of degree one on a curve over a finite field
Incidentally, (since you also explained this argument to me), you might be interested in Matt E's edit below. There's an extra step to get from "points of $\mathrm{Pic}^0$" to "line bundles on $C$" (which works in the case of a finite field).