scholarly journals On rational Eisenstein primes and the rational cuspidal groups of modular Jacobian varieties

2019 ◽  
Vol 372 (4) ◽  
pp. 2429-2466
Author(s):  
Hwajong Yoo
Keyword(s):  
Jacobian Varieties

Jacobian Varieties

1986 ◽  
pp. 167-212 ◽  
Author(s):  
J. S. Milne
Keyword(s):  
Jacobian Varieties

scholarly journals Abelian varieties attached to cycles of intermediate dimension

1979 ◽  
Vol 75 ◽  
pp. 95-119 ◽  
Author(s):  
Hiroshi Saito
Keyword(s):  
Abelian Variety ◽  
Projective Variety ◽  
Classical Case ◽  
Degree Zero ◽  
Algebraic Construction ◽  
Jacobian Varieties ◽  
Codimension One ◽  
Picard Variety ◽  
Complex Tori ◽  
Intermediate Jacobian

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.”

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

1982 ◽  
Vol 88 ◽  
pp. 197-212 ◽  
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].

Generalized Jacobian Varieties

1954 ◽  
Vol 59 (3) ◽  
pp. 505 ◽  
Author(s):  
Maxwell Rosenlicht
Keyword(s):  
Generalized Jacobian ◽  
Jacobian Varieties

On the Moduli of Jacobian Varieties

1960 ◽  
Vol 71 (2) ◽  
pp. 303 ◽  
Author(s):  
Walter L. Baily
Keyword(s):  
Jacobian Varieties

scholarly journals Computing functions on Jacobians and their quotients

2015 ◽  
Vol 18 (1) ◽  
pp. 555-577 ◽  
Author(s):  
Jean-Marc Couveignes ◽  
Tony Ezome
Keyword(s):  
Linear Time ◽  
Jacobian Varieties ◽  
Genus Two

We show how to efficiently evaluate functions on Jacobian varieties and their quotients. We deduce an algorithm to compute$(l,l)$isogenies between Jacobians of genus two curves in quasi-linear time in the degree$l^{2}$.

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