Erik Wallace

activity

20122018

most citedPrincipally polarized abelian surfaces with surjective galois representations on l-torsion

4 citations · 4 across the 3 of their papers we have counts for

collaborators

4 papers

math.NT2018

Bounds on the Mordell--Weil rank of elliptic curves over imaginary quadratic number fields with class number 1

Erik Wallace

We generalize the lemmas of Thomas Kretschmer to arbitrary number fields, and apply them with a 2-descent argument to obtain bounds for families of elliptic curves over certain ima…

math.NT2017

Bounds of the rank of the Mordell-Weil group of jacobians of hyperelliptic curves

Harris B. Daniels, Álvaro Lozano-Robledo, Erik Wallace

In this article we extend work of Shanks and Washington on cyclic extensions, and elliptic curves associated to the simplest cubic fields. In particular, we give families of exampl…

math.NT2015

Rank gain of Jacobians over finite Galois extensions

Bo-Hae Im, Erik Wallace

Let $X$ be a Riemann surface of genus $g > 0$ defined over a number field $K$ which is a degree $d$ -covering of $P_{K}^{1}$ . In this paper we show the existence of inf…

math.NT2012★ 4 cited

Principally polarized abelian surfaces with surjective galois representations on l-torsion

Erik Wallace

Given a rational variety $V$ defined over $K$ , we consider a principally polarized abelian variety $A$ of dimension $g$ defined over $V$ . For each prime l we then consider the galo…