An unconditional proof of the André-Oort conjecture for Hilbert modular surfaces (Q533694)

The authors give an unconditional proof of the André-Oort conjecture for Hilbert modular surfaces. The conjecture asserts that an irreducible curve contained in such a surface containing an infinite number of ``special points'' is itself ``special'' (references for these terms are given in the paper). Under the Generalised Riemann Hypothesis for imaginary quadratic fields, the result is due to \textit{B. Edixhoven} [Prog. Math. 195, 133--155 (2001; Zbl 1029.14007)]. The proof combines Galois-theoretic techniques with results from the theory of o-minimal structures, a part of model theory.