A simplified proof of the Andre-Oort conjecture for products of modular curves

Daw, C. ORCID: https://orcid.org/0000-0002-2488-6729 (2012) A simplified proof of the Andre-Oort conjecture for products of modular curves. Archiv der Mathematik, 98 (5). pp. 433-440. ISSN 0003-889X doi: 10.1007/s00013-012-0372-4

Abstract/Summary

In this paper we give a short proof of the André-Oort conjecture for products of modular curves under the Generalised Riemann Hypothesis using only simple Galois-theoretic and geometric arguments. We believe this method represents a strategy for proving the conjecture for a general Shimura variety under GRH without using ergodic theory. We also demonstrate a short proof of the Manin–Mumford conjecture for Abelian varieties using similar arguments.