Trinomials, singular moduli and Riffaut's conjecture

A singular modulus is the $j$-invariant of an elliptic curve with complex multiplication. Riffaut (2019) conjectured that a singular modulus of degree $h>2$ cannot be a root of a trinomial with rational coefficients. We show that this conjecture follows from the GRH, and obtain partial unconditional results. A joint work with Florian Luca and Amalia Pizarro.