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arXiv · 1905.05687

Ramification of Hilbert eigenvarieties at classical points

Chi-Yun Hsu
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Abstract

Andreatta-Iovita-Pilloni constructed eigenvarieties for cuspidal Hilbert modular forms. The eigenvariety has a natural map to the weight space, called the weight map. At a classical point, we compute a lower bound of the dimension of the tangent space of the fiber of the weight map using Galois deformation theory. Along with the classicality theorem due to Tian-Xiao, this enables us to characterize the classical points of the eigenvariety which are ramified over the weight space, in terms of the local splitting behavior of the associated Galois representation.

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Chi-Yun Hsu. 2019-05-14. Ramification of Hilbert eigenvarieties at classical points. https://arxiv.org/abs/1905.05687

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