Jonathan R. Love

activity

20192024

most citedSupersingular Curves With Small Non-integer Endomorphisms

12 citations · 13 across the 8 of their papers we have counts for

collaborators

8 papers

math.AG2024

Local and local-to-global Principles for zero-cycles on geometrically Kummer $K 3$ surfaces

Evangelia Gazaki, Jonathan Love

Let $X$ be a $K 3$ surface over a $p$ -adic field $k$ such that for some abelian surface $A$ isogenous to a product of two elliptic curves, there is an isomorphism over the algebraic…

math.AG2023

Hyperelliptic curves mapping to abelian varieties and applications to Beilinson's conjecture for zero-cycles

Evangelia Gazaki, Jonathan R. Love

Let $A$ be an abelian surface over an algebraically closed field $k$ with an embedding $k ↪ C$ . When $A$ is isogenous to a product of ell…

math.NT2023

On elements of prescribed norm in maximal orders of a quaternion algebra

Eyal Z. Goren, Jonathan R. Love

Let $O$ be a maximal order in the quaternion algebra over $Q$ ramified at $p$ and $\infty$ . We prove two theorems that allow us to recover the structure of $\mat…

math.AG2022

Torsion phenomena for zero-cycles on a product of curves over a number field

Evangelia Gazaki, Jonathan Love

For a smooth projective variety $X$ over a number field $k$ a conjecture of Bloch and Beilinson predicts that the kernel of the Albanese map of $X$ is a torsion group. In this arti…

math.NT2022

Root numbers of a family of elliptic curves and two applications

Jonathan Love

For each $t \in Q ∖ {- 1, 0, 1}$ , define an elliptic curve over $Q$ by \begin{align*} E_t:y^2=x(x+1)(x+t^2). \end{align*} Using a formula for the root number $…

math.AG2020

An arithmetic variant of Raynaud's theorem

Jonathan Love, Libby Taylor

It is well known that for a regular semistable curve $X$ over a DVR with algebraically closed residue field, the spanning trees of the dual graph of the special fiber of…

math.AG2020★ 1 cited

Rational Equivalences on Products of Elliptic Curves in a Family

Jonathan Love

Given a pair of elliptic curves $E_{1}, E_{2}$ over a field $k$ , we have a natural map $CH^{1} (E_{1})_{0} \otimes CH^{1} (E_{2})_{0} \to CH^{2} (E_{1} \times E_{2})$ , and a conjecture due t…

math.NT2019★ 12 cited

Supersingular Curves With Small Non-integer Endomorphisms

Jonathan Love, Dan Boneh

We introduce a special class of supersingular curves over $F_{p^{2}}$ , characterized by the existence of non-integer endomorphisms of small degree. A number of properties of…

Local and local-to-global Principles for zero-cycles on geometrically Kummer K3 surfaces