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學術專區

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演講
活動開始時間2017-12-11 16:00:00
活動結束時間2017-12-11 17:00:00
活動名稱學術演講-Nearly nilpotent groups and the Langlands reciprocity conjecture
主講者翁鵬絜 博士 (University of Lethbridge)
活動地點綜合三館4F Lecture Room B
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參考連結 
備註Abstract

Let $K/k$ be a Galois extension of number fields with group $G$, and let $rho$ be a non-trivial irreducible representation of $G$ of dimension $n$. In light of Artin reciprocity, Langlands conjectured that the Artin L-function attached to $rho$ is automorphic. This is often called the
Langlands reciprocity conjecture. Indeed, when $n=1$, this conjecture is exactly Artin reciprocity. Also, by the works of Langlands and many others, several significant progress has been made for $n=2$ and $n=4$. However, such a reciprocity conjecture is still open.

>From their theory of automorphic induction and the properties of nilpotent groups, Arthur and Clozel established Langlands reciprocity for any nilpotent $K/k$. In this talk, we shall emphasise how to use group theory to
study the Langlands reciprocity conjecture in much the same spirit of Arthur and Clozel. We shall introduce the notion of ``nearly nilpotent groups'', which can be seen as a generalisation of nilpotent groups (and abelian
groups). If time permits, we will explain how to obtain Langlands reciprocity for any nearly nilpotent $K/k$.
最後更新日期2017-12-05 14:02:35
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