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arXiv · 2206.15372

A local analogue of the ghost conjecture of Bergdall-Pollack

Ruochuan Liu·Nha Xuan Truong·Liang Xiao·Bin Zhao
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Abstract

We formulate a local analogue of the ghost conjecture of Bergdall and Pollack, which essentially relies purely on the representation theory of GL_2(Q_p). We further study the combinatorial properties of the ghost series as well as its Newton polygon, in particular, giving a characterization of the vertices of the Newton polygon and proving an integrality result of the slopes. In a forthcoming sequel, we will prove this local ghost conjecture under some mild hypothesis and give arithmetic applications.

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Ruochuan Liu, Nha Xuan Truong, Liang Xiao, Bin Zhao. 2022-06-30. A local analogue of the ghost conjecture of Bergdall-Pollack. https://arxiv.org/abs/2206.15372

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