学术报告

模曲线的p进刻画

发布人:发布时间: 2019-12-27

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题目:模曲线的p进刻画

报告人:左康 教授(德国 美因茨大学)

摘要:对于数域上的算术概型X, 我们定义算术周期性Higgs向量丛, 并提出一种针对这种向量丛和X上的motivic局部系之间的算术Simpson对应原理. 作为这一对应原理的一个例子, 我们证明仿射双曲曲线是模曲线当且仅当其上的一致化Higgs向量丛是周期性的并且其对应的F-晶体层的Frobenius迹生成的域是数域. 证明依赖于Abe证明的Deligne的p-l伴随猜想和Drinfeld关于函数域Langlands对应. 我们猜想算术Higgs向量丛的周期性能够推导出Frobenius迹生成域的有理性.这是与R.Krishnamoorthy和杨金榜合作的项目.

Summary:Given an arithmetic schemeover a number ring, we introduce the notion of arithmetic periodic Higgs bundle and propose an arithmetic Simpson correspondence between arithmetic periodic Higgs bundles and motivic local systems over . As a specialcase of this proposed correspondence we show, for example, an affine hyperbolic curve is a modular curve if and only the uniformization Higgs bundle is periodic and the frobenius trace field on the corresponding -isocrystal is rational. The proof relieson Deligne's conjecture ontocompanions solved by Abe and Drinfeld's work on Langlands correspondence over function field. 

We conjecture that the rationality of the frobenius trace field follows from the arithmetic periodicity of the Higgs bundle. This is a joint project with R. Krishnamoorthy and J.B. Yang.

时间:2019年12月30日下午15:00

地点:西大楼308

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