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See detailHilbert modular forms modulo p of partial weight one and unramifiedness of Galois representations
de Maria, Mariagiulia UL

Doctoral thesis (2020)

This thesis studies Hilbert modular forms of arbitrary weight with coefficients over a finite field of characteristic p. In particular, we compute the action on geometric q- expansions attached to these ... [more ▼]

This thesis studies Hilbert modular forms of arbitrary weight with coefficients over a finite field of characteristic p. In particular, we compute the action on geometric q- expansions attached to these forms of Hecke operators, including at places dividing p as constructed by Emerton, Reduzzi and Xiao. As an application, we prove that the Galois representation attached to a Hilbert cuspidal eigenform mod p, which has parallel weight 1 at a place P dividing p, is unramified at P. [less ▲]

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