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 1420-8938 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/70357
Identification Number/DOI	10.1007/s00013-012-0372-4
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
Download/View statistics	View download statistics for this item