UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ATTACHED TO HILBERT MODULAR FORMS MOD OF WEIGHT 1

Mladen Dimitrov, Gabor Wiese

Type: Article

Publication Date: 2018-04-23

Citations: 3

DOI: https://doi.org/10.1017/s1474748018000026

Abstract

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over $\overline{\mathbb{F}}_{p}$ of parallel weight 1 and level prime to $p$ is unramified above $p$ . This includes the important case of eigenforms that do not lift to Hilbert modular forms in characteristic 0 of parallel weight 1. The proof is based on the observation that parallel weight 1 forms in characteristic $p$ embed into the ordinary part of parallel weight $p$ forms in two different ways per prime dividing $p$ , namely via ‘partial’ Frobenius operators.

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Journal of the Institute of Mathematics of Jussieu - View
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Works Cited by This (42)

Action	Title	Year	Authors
+	Degeneration of Abelian Varieties	1990	Герд Фалтингс Ching-Li Chai
+	Arithmetic models for Hilbert modular varieties	1995	G. Pappas
+	p-Adic Automorphic Forms on Shimura Varieties	2004	Haruzo Hida
+	Hilbert Modular Forms	1990	Eberhard Freitag
+	Sur les représentations modulaires de degré 2 de Gal(Q¯/Q)	1987	Jean-Pierre Serre
+	Modularity Lifting Theorems beyond the Taylor-Wiles Method. II	2012	Frank Calegari David Geraghty
+	On ordinary ?-adic representations associated to modular forms	1988	Andrew Wiles
+	Hilbert modular forms: mod 𝑝 and 𝑝-adic aspects	2005	Fabrizio Andreatta Eyal Z. Goren
+	Some aspherical manifolds	1987	Michael W. Davis
+	A tameness criterion for Galois representations associated to modular forms (mod p)	1990	Benedict H. Gross