Quadratic torsion subgroups of modular Jacobian varieties

The group of cycles of codimension one algebraically equivalent to zero of a nonsingular projective variety modulo rational equivalence forms an abelian variety, i.e., the Picard variety. To the group of cycles of dimension zero and of degree zero, there corresponds an abelian variety, the Albanese variety. Similarly, Weil, Lieberman and Griffiths have attached complex tori to the cycles of intermediate dimension in the classical case. The aim of this article is to give a purely algebraic construction of such “intermediate Jacobian varieties.”

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On the fields of rationality for curves and for their jacobian varieties

Nagoya Mathematical Journal ◽

10.1017/s0027763000020171 ◽

1982 ◽

Vol 88 ◽

pp. 197-212 ◽

Cited By ~ 2

Author(s):

Tsutomu Sekiguchi

Keyword(s):

Hyperelliptic Curve ◽

Partial Result ◽

Jacobian Variety ◽

Noetherian Scheme ◽

Jacobian Varieties ◽

Field Of Moduli ◽

The One

Throughout the paper, a scheme means a noetherian scheme. By a curve C over a scheme S of genus g, we mean a proper and smooth S-scheme with irreducible curves of genus g as geometric fibres. In the previous paper [15], the author showed that the field of moduli for a non-hyperelliptic curve over a field coincides with the one for its canonically polarized jacobian variety, and in [16], he gave a partial result on the coincidence of the fields of rationality for a hyperelliptic curve and for its canonically polarized jacobian variety. In the present paper, we will discuss the isomorphy of the isomorphism schemes of two curves over a scheme and of their canonically polarized jacobian schemes, by using Oort-Steenbrink’s result [12].

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Decomposition of Jacobian Varieties and Dirichlet Series of Hecke Type

American Journal of Mathematics ◽

10.2307/2373368 ◽

1970 ◽

Vol 92 (3) ◽

pp. 671 ◽

Cited By ~ 1

Author(s):

Toshitsune Miyake

Keyword(s):

Dirichlet Series ◽

Jacobian Varieties

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