scholarly journals Simplicial volume of Hilbert modular varieties

2009 ◽  
pp. 457-470 ◽  
Author(s):  
Clara Löh ◽  
Roman Sauer
Keyword(s):  
Simplicial Volume ◽  
Hilbert Modular ◽  
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

scholarly journals Finite descent obstruction for Hilbert modular varieties

2020 ◽  
pp. 1-22
Author(s):  
Gregorio Baldi ◽  
Giada Grossi
Keyword(s):  
Real Field ◽  
Absolute Galois Group ◽  
Hodge Conjecture ◽  
Hilbert Modular ◽  
Finite Set ◽  
The Absolute ◽  
Hilbert Modular Varieties ◽  
Totally Real ◽  
Modular Varieties ◽  
Special Case

Abstract Let S be a finite set of primes. We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of $\mathbb {Z}_{S}$ -points on integral models of Hilbert modular varieties, extending a result of D. Helm and F. Voloch about modular curves. Let L be a totally real field. Under (a special case of) the absolute Hodge conjecture and a weak Serre’s conjecture for mod $\ell $ representations of the absolute Galois group of L, we prove that the same holds also for the $\mathcal {O}_{L,S}$ -points.

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