Assuming Lang-Trotter-type sparsity for simultaneous supersingular reductions, the paper proves two Zilber-Pink-type finiteness results for Hodge generic curves in Y(1)^n via André's G-function method.
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Lang-Trotter conjecture for elliptic curve pairs implies new Zilber-Pink cases for curves in A_3 via André's G-functions method, without boundary intersection assumptions.
Proves explicit Gross-Zagier formula linking CM point heights on E_{p^i} to L-function derivatives for the 4,7 cases of Sylvester's conjecture.
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Supersingular reduction and strongly special intersections in powers of the modular curve
Assuming Lang-Trotter-type sparsity for simultaneous supersingular reductions, the paper proves two Zilber-Pink-type finiteness results for Hodge generic curves in Y(1)^n via André's G-function method.
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Lang-Trotter phenomena and unlikely intersections
Lang-Trotter conjecture for elliptic curve pairs implies new Zilber-Pink cases for curves in A_3 via André's G-functions method, without boundary intersection assumptions.
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Gross-Zagier formula for the $4, 7$ cases of Sylvester's conjecture
Proves explicit Gross-Zagier formula linking CM point heights on E_{p^i} to L-function derivatives for the 4,7 cases of Sylvester's conjecture.