Bruce W. Jordan

activity

19982025

most citedAbelian varieties isogenous to a power of an elliptic curve

23 citations · 45 across the 19 of their papers we have counts for

collaborators

21 papers

math.CO2025

Generalized Jacobians of graphs

Bruce W. Jordan, Kenneth A. Ribet, Anthony J. Scholl

We define a generalized Jacobian $J_{m} (Gr)$ and a generalized Picard group $P_{m} (Gr)$ of a graph $Gr$ with respect…

math.NT2023

A composition law and refined notions of convergence for periodic continued fractions

Bradley W. Brock, Bruce W. Jordan, Lawren Smithline

We define an equivalence relation on periodic continued fractions with partial quotients in a ring $O \subseteq C$ , a group law on these equivalence classes, and…

math.AG2022★ 1 cited

Modular curves and Néron models of generalized Jacobians

Bruce W. Jordan, Kenneth A. Ribet, Anthony J. Scholl

Let $X$ be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring $R$ , and $m$ a modulus on $X$ , given by a closed su…

math.NT2022

Isogeny complexes of superspecial abelian varieties

Bruce W. Jordan, Yevgeny Zaytman

We consider the structures formed by isogenies of abelian varieties with polarizations that are not necessarily principal, specifically with the $[ℓ]$ -polarizations we have prev…

math.NT2021

Isogeny graphs of superspecial abelian varieties

Bruce W. Jordan

We define three different isogeny graphs of principally polarized superspecial abelian varieties, prove foundational results on them, and explain their role in number theory and ge…

math.NT2020

Linear independence in linear systems on elliptic curves

Bradley W. Brock, Bruce W. Jordan, Bjorn Poonen +2

Let $E$ be an elliptic curve, with identity $O$ , and let $C$ be a cyclic subgroup of odd order $N$ , over an algebraically closed field $k$ with $char k ∤ N$ . For…