Abstract.
Let N be a square free integer, prime to 6. Let φ the imbeding of X 0(N) in its Jacobian relative to the point ∞. We show that the set is finite and that is infinite. This explicit form of the Bogomolov conjecture is obtained by an estimation of the self-intersection of the dualizing sheaf, in the sense of Arakelov theory, of modular curves. This result is obtained by estimating several quantities attached to the Arakelov metric on X 0(N), starting with Petersson's trace formula
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Oblatum 1-I-1997 & 30-IV-1997
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Michel, P., Ullmo, E. Points de petite hauteur sur les courbes modulaires X0(N). Invent math 131, 645–674 (1998). https://doi.org/10.1007/s002220050216
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DOI: https://doi.org/10.1007/s002220050216