Hilbert modular forms modulo p of partial weight one and unramifiedness of Galois representations

English

de Maria, Mariagiulia[University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]

14-Sep-2020

University of Luxembourg, Luxembourg

DOCTEUR DE L’UNIVERSITÉ DU LUXEMBOURG EN MATHÉMATIQUES

106

Wiese, Gabor

Dimitrov, Mladen

Debes, Pierre

Perucca, Antonella

Xiao, Liang

Diamond, Fred

[en] Hilbert Modular Forms ; Partial Weight One ; Langlands Program

[en] 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.