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Degree of an isogeny in the endomorphism ring of the jacobian of a curve and self intersection index in its ring of correspondences

I hope this question is not too basic. Let $C/\bar{k}$ be a nonsingular irreducible curve of genus $g$ and $\mathfrak{C}(C\times C)\cong \text{CH}^1(C\times C)$ be its ring of correspondences. I am ...
Eduardo R. Duarte's user avatar