Congruences between automorphic forms

自同构形式之间的同余

• 批准号: EP/G050511/1
• 负责人: Shu Sasaki
• 金额: $ 29.17万
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2009
• 资助国家: 英国
• 起止时间: 2009 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FG050511%2F1
• 关键词: Congruences; between; automorphic; forms

I propose to prove new cases of the strong Artin conjecture for totally odd two dimensional representations of the Galois group of a totally real field. More precisely, I propose to establish ``analytic continuation of overconvergent Hilbert modular eigenforms'' in the inert Hilbert case and generalise the main theorem of Buzzard-Taylor to the Hilbert case. Mimicking the approach of Taylor's ``Artin II'' paper, one should get modularity of certain mod p Galois representations subject to some local conditions, and many cases of Artin's conjecture should then become accessible. Secondly, I propose to show that there is another example of the correspondence predicted by Langlands between n-dimensional representations of the absolute Galois group of the rationals Q and (cuspidal) automorphic representations of GL(n) over Q. Following the geometric argument of Kisin-Lai for Hilbert modular forms, it should be possible to construct p-adic analytic families of automorphic Galois representations and associaten-dimensional Galois representations by ``specialisation'' to non-regular algebraic automorphic representations of GL(n) over Q (whose Hodge-Tate weights ``at infinity'' are not necessarily distinct). It may also be possible toprove that non-regular automorphic representations for GL(n) appear on the Chenevier's eigenvariety and associate Galois representations by specialising families of Galois representations Chenevier constructed. Another approach to look at congruences between automorphic forms of ``regular weight'' and ``non-regular weight'', analogous to Deligne-Serre, will also be considered.

我建议证明对完全真实领域的Galois组的完全奇怪的二维表示，这是强烈的Artin猜想的新案例。更确切地说，我建议在惰性希尔伯特案中建立``分析性延续过度会议的希尔伯特模块化特征形式''，并将Buzzard-Taylor的主要定理推广到Hilbert案。模仿泰勒（Taylor）的``Artin II''纸的方法，应该获得某些MOD P GALOIS表示的模块化，并在某些地方条件下，许多Artin猜想的案例应该可以访问。其次，我建议表明，兰格兰兹在Q的绝对galois组的n维表示和（cuspidal的）自动形态表示Q的n维表示之间有另一个例子。通过``专业化''的辅助剂维galois表示，``''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''在Q上的gl（n）（其hodge-tate权重``infinity in Infinity'''不一定是不同的）。也有可能topRove是，GL（N）的非规范自动形态表示出现在Chenevier的特征变量和通过专门化Galois代表家族Chenevier构建的家族中。还将考虑另一种观察``常规重量''和````''''''''''和``定期重量''与``非规则重量''之间的一致性了。