8 citations · 14 across the 6 of their papers we have counts for
5 papers · 1 filter
Galois Groups Via Atkin-Lehner Twists
Pete L. Clark
Using Serre's proposed complement to Shih's Theorem, we obtain PSL_2(F_p) as a Galois group over Q for at least 614 new primes p. Under the assumption that rational elliptic curves…
There are genus one curves of every index over every number field
Pete L. Clark
We show that there exist genus one curves of every index over the rational numbers, answering affirmatively a question of Lang and Tate. The proof is "elementary" in the sense that…
Bounds for torsion on abelian varieties with integral moduli
Pete L. Clark
We give a function F(d,n,p) such that if K/Q_p is a degree n field extension and A/K is a d-dimensional abelian variety with potentially good reduction, then #A(K)[tors] is at most…
The period-index problem in WC-groups II: abelian varieties
Pete L. Clark
We study the relationship between the period and the index of a principal homogeneous space over an abelian variety, obtaining results which generalize work of Cassels and Lichtenb…
The period-index problem in WC-groups I: elliptic curves
Pete L. Clark
Let E/K be an elliptic curve defined over a number field, and let p be a prime number such that E(K) has full p-torsion. We show that the order of the p-part of the Shafarevich-Tat…