Allan Keeton

activity

20162020

most citedAbelian varieties isogenous to a power of an elliptic curve

23 citations · 23 across the 4 of their papers we have counts for

collaborators

5 papers

math.NT2020

Quotient graphs and amalgam presentations for unitary groups over cyclotomic rings

Colin Ingalls, Bruce W. Jordan, Allan Keeton +2

Suppose $4∣ n$ , $n \geq 8$ , $F = F_{n} = Q (ζ_{n} + ζ ˉ_{n})$ , and there is one prime $p = p_{n}$ above $2$ in $F_{n}$ . We study amalgam presentations for $\operatornam…

math.NT2019

Sarnak's conjecture in quantum computing, cyclotomic unitary group coranks, and Shimura curves

Colin Ingalls, Bruce W. Jordan, Allan Keeton +2

Sarnak's conjecture in quantum computing concerns when the groups $PU_{2}$ and $PSU_{2}$ over cyclotomic rings $Z [ζ_{n}, 1/2]$ with $ζ_{n} = e^{2 π i / n}$ …

math.NT2019

The Clifford-cyclotomic group and Euler-Poincaré characteristics

Colin J. Ingalls, Bruce W. Jordan, Allan Keeton +2

For an integer $n \geq 8$ divisible by $4$ , let $R_{n} = Z [ζ_{n}, 1/2]$ and let $U_{2} (R_{n})$ be the group of $2 \times 2$ unitary matrices with entries in $R_{n}$ . Set $…

math.AG2016

Unique factorization of principally polarized abelian varieties

Bruce W. Jordan, Allan G. Keeton, Bjorn Poonen

Shimura proved that each principally polarized abelian variety over $C$ admits a unique factorization into irreducible principally polarized abelian varieties. We give an…

math.AG2016★ 23 cited

Abelian varieties isogenous to a power of an elliptic curve

Bruce W. Jordan, Allan G. Keeton, Bjorn Poonen +3

Let $E$ be an elliptic curve over a field $k$ . Let $R := End E$ . There is a functor $H om_{R} (-, E)$ from the category of finitely presented torsion-free…