The Clifford-cyclotomic group and Euler–Poincaré characteristics

Autor: Bruce W. Jordan, Allan Keeton, Yevgeny Zaytman, Colin Ingalls, Adam Logan

Publikováno v: Canadian Mathematical Bulletin. 64:651-666

For an integer $n\geq 8$ divisible by $4$ , let $R_n={\mathbb Z}[\zeta _n,1/2]$ and let $\operatorname {\mathrm {U_{2}}}(R_n)$ be the group of $2\times 2$ unitary matrices with entries in $R_n$ . Set $\operatorname {\mathrm {U_2^\zeta }}(R_n)=\{\gamm

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https://doi.org/10.4153/s0008439520000727

Quotient graphs and amalgam presentations for unitary groups over cyclotomic rings

Autor: Allan Keeton, Colin Ingalls, Yevgeny Zaytman, Bruce W. Jordan, Adam Logan

Suppose $4|n$, $n\geq 8$, $F=F_n=\mathbb{Q}(\zeta_n+\bar{\zeta}_n)$, and there is one prime $\mathfrak{p}=\mathfrak{p}_n$ above $2$ in $F_n$. We study amalgam presentations for $\operatorname{PU_{2}}(\mathbb{Z}[\zeta_n, 1/2])$ and $\operatorname{PSU_

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http://arxiv.org/abs/2001.01695

The analytic class number formula for 1‐dimensional affine schemes

Autor: Bruce W. Jordan, Bjorn Poonen

Publikováno v: arXiv

We derive an analytic class number formula valid for an order in a product of $S$-integers in global fields, or equivalently for reduced finite-type affine schemes of pure dimension $1$ over $\mathbb{Z}$.
Comment: 15 pages; a second example, of

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https://hdl.handle.net/1721.1/134036

Integral points on varieties defined by matrix factorization into elementary matrices

Autor: Bruce W. Jordan, Yevgeny Zaytman

Let K be a number field and S be a finite set of valuations of K containing the archimedean valuations. Let O be the ring of S-integers. For A ∈ S L 2 ( O ) and k ≥ 1 , we define matrix-factorization varieties V k ( A ) over O which parametrize f

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Abelian varieties isogenous to a power of an elliptic curve

Autor: Bjorn Poonen, Eric M. Rains, Allan Keeton, N.I. Shepherd-Barron, Bruce W. Jordan, John Tate

Publikováno v: arXiv
Jordan, B W, Keeton, A G, Poonen, B, Rains, E M, Shepherd-Barron, N & Tate, J T 2018, ' Abelian varieties isogenous to a power of an elliptic curve ', COMPOSITIO MATHEMATICA, vol. 154, no. 5, pp. 934-959 . https://doi.org/10.1112/S0010437X17007990

Let $E$ be an elliptic curve over a field $k$. Let $R:= \text{End}\, E$. There is a functor $\mathscr{H}\!\!\mathit{om}_R(-,E)$ from the category of finitely presented torsion-free left $R$-modules to the category of abelian varieties isogenous to a

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