scholarly journals Families of absolutely simple hyperelliptic jacobians

2009 ◽  
Vol 100 (1) ◽  
pp. 24-54 ◽  
Author(s):  
Yuri G. Zarhin
Keyword(s):  
Hyperelliptic Jacobians

scholarly journals Canonical heights and division polynomials

2014 ◽  
Vol 157 (2) ◽  
pp. 357-373 ◽  
Author(s):  
ROBIN de JONG ◽  
J. STEFFEN MÜLLER
Keyword(s):  
Recurrence Relation ◽  
Number Field ◽  
Diophantine Approximation ◽  
New Method ◽  
Approximation Result ◽  
Algebraic Point ◽  
Canonical Height ◽  
Division Polynomials ◽  
Genus 2 ◽  
Hyperelliptic Jacobians

AbstractWe discuss a new method to compute the canonical height of an algebraic point on a hyperelliptic jacobian over a number field. The method does not require any geometrical models, neitherp-adic nor complex analytic ones. In the case of genus 2 we also present a version that requires no factorisation at all. The method is based on a recurrence relation for the ‘division polynomials’ associated to hyperelliptic jacobians, and a diophantine approximation result due to Faltings.

scholarly journals Hyperelliptic jacobians with real multiplication

2006 ◽  
Vol 117 (1) ◽  
pp. 53-86 ◽  
Author(s):  
Arsen Elkin
Keyword(s):  
Real Multiplication ◽  
Hyperelliptic Jacobians

A characterization of hyperelliptic Jacobians

1993 ◽  
Vol 79 (1) ◽  
pp. 335-341
Author(s):  
Giambattista Marini
Keyword(s):  
Hyperelliptic Jacobians

scholarly journals Hyperelliptic Jacobians and isogenies

2018 ◽  
Vol 335 ◽  
pp. 896-909 ◽  
Author(s):  
J.C. Naranjo ◽  
G.P. Pirola
Keyword(s):  
Hyperelliptic Jacobians
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