Isogeny graphs of superspecial abelian varieties

Bruce W. Jordan

Isogeny graphs of superspecial abelian varieties

Number Theory 2021-05-04 v2 Algebraic Geometry

Authors: Bruce W. Jordan

Abstract

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 geometry. This is background to joint work with Yevgeny Zaytman on properties of these isogeny graphs for dimension $g>1$ , especially the result that these graphs are connected, but not in general Ramanujan.

Keywords

isogeny graphs superspecial abelian varieties principally polarized number theory ramanujan graphs connectedness

Cite

@article{arxiv.2101.01579,
  title  = {Isogeny graphs of superspecial abelian varieties},
  author = {Bruce W. Jordan},
  journal= {arXiv preprint arXiv:2101.01579},
  year   = {2021}
}

Comments

This is the write-up of a lecture delivered 15 October 2020 in the conference supersingular2020 at RIMS, Kyoto. It draws from arXiv:2005.09031v4. arXiv admin note: text overlap with arXiv:2005.09031

Isogeny graphs of superspecial abelian varieties

Abstract

Keywords

Cite

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