Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms
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DOI: 10.1007/s00222-018-0825-x
Abstract: We prove the strong Artin conjecture for continuous, totally odd, two-dimensional representations of the absolute Galois group of a totally real field F. read more here.
Keywords: models hilbert; ramified case; modular varieties; varieties ramified ... See more keywords
Central values of twisted base change L-functions associated to Hilbert modular forms
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DOI: 10.1016/j.jnt.2018.03.005
Abstract: We use relative trace formula to prove a non-vanishing result and a subconvexity result for the twisted base change $L$-functions associated to Hilbert modular forms whose local components at ramified places are some supercuspidal representations.… read more here.
Keywords: change functions; associated hilbert; functions associated; twisted base ... See more keywords
UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES
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DOI: 10.1017/fms.2017.26
Abstract: Let $p$ be a prime number and $F$ a totally real number field. For each prime $\mathfrak{p}$ of $F$ above $p$ we construct a Hecke operator $T_{\mathfrak{p}}$ acting on $(\text{mod}\,p^{m})$ Katz Hilbert modular classes which… read more here.
Keywords: unramifiedness galois; arising hilbert; galois representations; hilbert modular ... See more keywords
On the eigenvariety of Hilbert modular forms at classical parallel weight one points with dihedral projective image
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DOI: 10.1090/tran/7064
Abstract: We show that the p-adic eigenvariety constructed by AndreattaIovita-Pilloni, parameterizing cuspidal Hilbert modular eigenforms defined over a totally real field F , is smooth at certain classical parallel weight one points which are regular at… read more here.
Keywords: parallel weight; weight one; eigenvariety; one points ... See more keywords
The structure of mixed weight Hilbert modular forms
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DOI: 10.1142/s0129167x19500083
Abstract: In this paper, we determine the structure of some modules of mixed weight Hilbert modular forms. We mainly discuss Hilbert modular forms with discriminant 5 and then with discriminant 8 in the last section. read more here.
Keywords: hilbert modular; weight hilbert; modular forms; mixed weight ... See more keywords