Mod $p$ Hilbert modular forms of parallel weight one: the ramified case

Payman L Kassaei

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arXiv · 1711.01680

Mod $p$ Hilbert modular forms of parallel weight one: the ramified case

Payman L Kassaei

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Abstract

We generalize the main result of arXiv:1206.6631 [math.NT] to all totally real fields. In other words, for $p>2$ prime, we prove (under a mild Taylor-Wiles hypothesis) that if a modular representation is unramified and $p$-distinguished at all places above $p$, then it arises from a mod $p$ Hilbert modular form of parallel weight one. This (mostly) resolves the weight one part of Serre's conjecture for totally real fields.

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Payman L Kassaei. 2017-11-06. Mod $p$ Hilbert modular forms of parallel weight one: the ramified case. https://arxiv.org/abs/1711.01680

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