We study the 2‐parity conjecture for Jacobians of hyperelliptic curves over number fields.
Under some mild assumptions on their reduction, we prove the conjecture over quadratic …

Let be an integer, a number field, the integral closure of in and a positive multiple of. The
article deals with degree polynomials such that the superelliptic curve has twists without …

En supposant la conjecture ABC, nous utilisons un travail de Granville pour montrer qu'une
courbe hyperelliptique C/Q de genre au moins trois a une infinité de tordues quadratiques …

In his paper, Rational Points On Modular Curves, Barry Mazur stated the following program,
which is now known as Mazur's Program B:“Given a number field K and a subgroup H of …

Conditionally on the abc conjecture, we generalize the previous work of Clark and the
author to show that a superelliptic curve C: yn= f (x) of sufficiently high genus has infinitely …

Nagao's conjecture relates the rank of an elliptic surface to a limit formula arising from a
weighted average of fibral Frobenius traces, and it is further generalized to smooth …

Let $ K $ be a complete discrete valuation field with ring of integers $ R $ and residue field $
k $ of characteristic $ p> 2$. We assume moreover that $ k $ is algebraically closed. Let $ C …

Let F be a number field, OF the integral closure of ℤ in F, and P (T)∈ OF [T] a monic
separable polynomial such that P (0)≠ 0 and P (1)≠ 0. We give precise sufficient conditions …

Hasse Principle Violations in Twist Families of Hyperelliptic and Superelliptic Curves by Lori
Desirae Watson (Under the Directi Page 1 Hasse Principle Violations in Twist Families of …

Hasse Principle Violations of Quadratic Twists of Hyperelliptic Curves Page 1 Hasse Principle
Violations of Quadratic Twists of Hyperelliptic Curves Lori Watson Joint work with Pete Clark …