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- Title
UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES.
- Authors
EMERTON, MATTHEW; REDUZZI, DAVIDE; LIANG XIAO
- Abstract
Let p be a prime number and F a totally real number field. For each prime p of F above p we construct a Hecke operator Tp acting on (mod pm) Katz Hilbert modular classes which agrees with the classical Hecke operator at p for global sections that lift to characteristic zero. Using these operators and the techniques of patching complexes of Calegari and Geraghty we prove that the Galois representations arising from torsion Hilbert modular classes of parallel weight 1 are unramified at p when [F : Q] = 2. Some partial and some conjectural results are obtained when [F : Q] > 2.
- Subjects
GALOIS theory; HECKE operators; HILBERT modular surfaces; OPERATOR algebras; LOGICAL prediction
- Publication
Forum of Mathematics, Sigma, 2017, Vol 5, p1
- ISSN
2050-5094
- Publication type
Article
- DOI
10.1017/fms.2017.26