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This is going to be a fairly vague question but hopefully it will have concrete answers: There is this recurrent phenomenon in the arithmetic of curves (possibly stacky,affine) where there is a "...

I read somewhere that if $X$ is a projective variety of general type over a number field $K$, then rational points are an analogue of entire curves $\mathbf{C}\to X^{an}$ (with $X^{an}$ the ...