scholarly journals FIELDS OF MODULI OF CLASSICAL HUMBERT CURVES

2011 ◽  
Vol 63 (4) ◽  
pp. 919-930 ◽  
Author(s):  
R. A. Hidalgo ◽  
S. Reyes
Keyword(s):  
Fields Of Moduli

scholarly journals Erratum to: Fields of moduli and definition of hyperelliptic covers

2013 ◽  
Vol 101 (6) ◽  
pp. 599-600
Author(s):  
Yolanda Fuertes ◽  
Gabino González-Diez
Keyword(s):  
Definition Of ◽  
Fields Of Moduli

Fields of moduli of some special curves

2016 ◽  
Vol 220 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Ruben A. Hidalgo ◽  
Saúl Quispe
Keyword(s):  
Fields Of Moduli

Fields of moduli and definition of hyperelliptic covers

2006 ◽  
Vol 86 (5) ◽  
pp. 398-408 ◽  
Author(s):  
Y. Fuertes ◽  
G. González-Diez
Keyword(s):  
Definition Of ◽  
Fields Of Moduli

Galois Representations Over Fields of Moduli and Rational Points on Shimura Curves

2014 ◽  
Vol 66 (5) ◽  
pp. 1167-1200 ◽  
Author(s):  
Victor Rotger ◽  
Carlos de Vera-Piquero
Keyword(s):  
Abelian Variety ◽  
Moduli Space ◽  
Quadratic Field ◽  
Galois Representations ◽  
Abelian Varieties ◽  
Main Idea ◽  
Galois Representation ◽  
Rational Points ◽  
Shimura Curves ◽  
Fields Of Moduli

AbstractThe purpose of this note is to introduce a method for proving the non-existence of rational points on a coarse moduli space X of abelian varieties over a given number field K in cases where the moduli problem is not fine and points in X(K) may not be represented by an abelian variety (with additional structure) admitting a model over the field K. This is typically the case when the abelian varieties that are being classified have even dimension. The main idea, inspired by the work of Ellenberg and Skinner on the modularity of ℚ-curves, is that one may still attach a Galois representation of Gal(/K) with values in the quotient group GL(Tℓ(A))/ Aut(A) to a point P = [A] ∈ X(K) represented by an abelian variety A/, provided Aut(A) lies in the centre of GL(Tℓ(A)). We exemplify our method in the cases where X is a Shimura curve over an imaginary quadratic field or an Atkin–Lehner quotient over ℚ.

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