Degrees of strongly special subvarieties and the André–Oort conjecture

Daw, C. ORCID: https://orcid.org/0000-0002-2488-6729 (2016) Degrees of strongly special subvarieties and the André–Oort conjecture. Journal für die reine und angewandte Mathematik (Crelles Journal), 2016 (721). pp. 81-108. ISSN 0075-4102 doi: 10.1515/crelle-2014-0062

Abstract/Summary

In this paper we give a new proof of the André–Oort conjecture under the generalised Riemann hypothesis. In fact, we generalise the strategy pioneered by Edixhoven, and implemented by Klingler and Yafaev, to all special subvarieties. Thus, we remove ergodic theory from the proof of Klingler, Ullmo and Yafaev and replace it with tools from algebraic geometry. Our key ingredient is a lower bound for the degrees of strongly special subvarieties coming from Prasad’s volume formula for S-arithmetic quotients of semisimple groups.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/70360
Identification Number/DOI	10.1515/crelle-2014-0062
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	De Gruyter
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