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arXiv · 2606.25485

Prescribed lifts of 2-dimensional representations

Matthew Emerton·Toby Gee·Lue Pan·Xinwen Zhu
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Abstract

Let F be a totally real field, and let p be prime. Under standard Taylor--Wiles hypotheses, we show that an irreducible, 2-dimensional, totally odd mod p representation of the absolute Galois group of F admits lifts lying on arbitrary prescribed components of local deformation rings, allowing potentially semistable conditions with arbitrary regular Hodge--Tate weights.

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Matthew Emerton, Toby Gee, Lue Pan, Xinwen Zhu. 2026-06-24. Prescribed lifts of 2-dimensional representations. https://arxiv.org/abs/2606.25485

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