Degrees of strongly special subvarieties and the André–Oort conjecture
Degrees of strongly special subvarieties and the André–Oort conjecture
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强特殊子族的度和安德烈-奥尔特猜想
DOI：
10.1515/crelle-2014-0062
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Christopher Daw
中科院分区：
文献类型：
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作者：
Christopher Daw
本文在广义黎曼假设下给出了Andre-Oort猜想的一个新证明。事实上，我们概括的战略开创了Edixhoven，并实施了Klingler和Yafaev，所有特殊的子品种。因此，我们删除遍历理论的证明Klingler，Ullmo和Yafaev，并取代它的工具，从代数几何。我们的关键成分是一个下界的程度强特殊的子品种来自Prasad的体积公式的S-算术代数的半单群。
In this paper we give a new proof of the Andre–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.