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Isogeny graphs of superspecial abelian varieties

2021/01/05 by Bruce W. Jordan, Jordan, Bruce W.
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography #math.AG #math.NT #msc:11G10 #msc:14G15 #msc:14K02

paper · pdf · doi:10.48550/arxiv.2101.01579

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

arxiv created 2021/04/30 · arxiv updated 2021/05/04

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.

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