scholarly journals Integral models of Hilbert modular varieties in the ramified case, deformations of modular Galois representations, and weight one forms

2018 ◽  
Vol 215 (1) ◽  
pp. 171-264
Author(s):  
Shu Sasaki
Keyword(s):  
Galois Representations ◽  
Hilbert Modular ◽  
Weight One ◽  
Hilbert Modular Varieties ◽  
Modular Varieties

scholarly journals Minimal weights of Hilbert modular forms in characteristic

2017 ◽  
Vol 153 (9) ◽  
pp. 1769-1778 ◽  
Author(s):  
Fred Diamond ◽  
Payman L Kassaei
Keyword(s):  
Modular Forms ◽  
Real Field ◽  
Hilbert Modular Forms ◽  
Hilbert Modular ◽  
Hilbert Modular Varieties ◽  
Totally Real ◽  
Modular Varieties ◽  
Totally Real Field

We consider mod $p$ Hilbert modular forms associated to a totally real field of degree $d$ in which $p$ is unramified. We prove that every such form arises by multiplication by partial Hasse invariants from one whose weight (a $d$-tuple of integers) lies in a certain cone contained in the set of non-negative weights, answering a question of Andreatta and Goren. The proof is based on properties of the Goren–Oort stratification on mod $p$ Hilbert modular varieties established by Goren and Oort, and Tian and Xiao.

scholarly journals ALGEBRAIC CYCLES AND TATE CLASSES ON HILBERT MODULAR VARIETIES

2014 ◽  
Vol 10 (01) ◽  
pp. 161-176
Author(s):  
JAYCE R. GETZ ◽  
HEEKYOUNG HAHN
Keyword(s):  
Discrete Series ◽  
Algebraic Cycles ◽  
Automorphic Representation ◽  
Abelian Extensions ◽  
Real Place ◽  
Hilbert Modular ◽  
Rank One ◽  
Hilbert Modular Varieties ◽  
Totally Real ◽  
Modular Varieties

Let E/ℚ be a totally real number field that is Galois over ℚ, and let π be a cuspidal, nondihedral automorphic representation of GL 2(𝔸E) that is in the lowest weight discrete series at every real place of E. The representation π cuts out a "motive" M ét (π∞) from the ℓ-adic middle degree intersection cohomology of an appropriate Hilbert modular variety. If ℓ is sufficiently large in a sense that depends on π we compute the dimension of the space of Tate classes in M ét (π∞). Moreover if the space of Tate classes on this motive over all finite abelian extensions k/E is at most of rank one as a Hecke module, we prove that the space of Tate classes in M ét (π∞) is spanned by algebraic cycles.

scholarly journals Stratifying Lie Strata of Hilbert Modular Varieties

2020 ◽  
Vol 24 (6) ◽  
pp. 1307-1352
Author(s):  
Chia-Fu Yu ◽  
Ching-Li Chai ◽  
Frans Oort
Keyword(s):  
Hilbert Modular ◽  
Hilbert Modular Varieties ◽  
Modular Varieties
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