Multi-tensors of differential forms on the Hilbert modular variety and on its subvarieties

1986 ◽  
Vol 274 (4) ◽  
pp. 659-670 ◽  
Author(s):  
Shigeaki Tsuyumine
Keyword(s):  
Differential Forms ◽  
Modular Variety ◽  
Hilbert Modular ◽  
Hilbert Modular Variety

scholarly journals On Ihara’s lemma for Hilbert modular varieties

2009 ◽  
Vol 145 (5) ◽  
pp. 1114-1146 ◽  
Author(s):  
Mladen Dimitrov
Keyword(s):  
Selmer Group ◽  
Absolute Galois Group ◽  
Modular Variety ◽  
Low Weight ◽  
Hilbert Modular ◽  
Finite Set ◽  
Hilbert Modular Varieties ◽  
Totally Real ◽  
Modular Varieties ◽  
Hilbert Modular Variety

AbstractLet ρ be a two-dimensional modulo p representation of the absolute Galois group of a totally real number field. Under the assumptions that ρ has a large image and admits a low-weight crystalline modular deformation we show that any low-weight crystalline deformation of ρ unramified outside a finite set of primes will be modular. We follow the approach of Wiles as generalized by Fujiwara. The main new ingredient is an Ihara-type lemma for the local component at ρ of the middle degree cohomology of a Hilbert modular variety. As an application we relate the algebraic p-part of the value at one of the adjoint L-function associated with a Hilbert modular newform to the cardinality of the corresponding Selmer group.

Effective resolution of cusps on Hilbert modular varieties

1986 ◽  
Vol 99 (1) ◽  
pp. 51-57
Author(s):  
G. K. Sankaran
Keyword(s):  
Modular Variety ◽  
Hilbert Modular ◽  
Hilbert Modular Varieties ◽  
Modular Varieties ◽  
Hilbert Modular Variety

In this paper, we use the Shintani decomposition, known to number theorists, to describe an effective method of finding a resolution of the cusps of a Hilbert modular variety, in any dimension.

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