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See detailUnramifiedness of Galois representations attached to weight one Hilbert modular eigenforms mod p
Dimitrov, Mladen; Wiese, Gabor UL

in Journal of the Institute of Mathematics of Jussieu (2020), 19(2), 281-306

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This ... [more ▼]

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar 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. MSC: 11F80 (primary); 11F41, 11F33 Keywords: Hilbert modular forms modulo p, weight one, Galois representations [less ▲]

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See detailReductions of points on algebraic groups
Lombardo, Davide; Perucca, Antonella UL

in Journal of the Institute of Mathematics of Jussieu (2019)

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See detailMicrolocal Euler classes and Hochschild homology
Masaki, Kashiwara; Schapira, Pierre UL

in Journal of the Institute of Mathematics of Jussieu (2014), 13(3), 486-516

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