Geodesic
Quasi-isogeny groups of supersingular abelian surfaces via pro-étale fundamental groups
Documenta mathematica, Tome 28 (2023) no. 5, pp. 1053-1078

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We consider a Jb​(Qp​) on the supersingular locus of the Siegel threefold constructed by Caraiani–Scholze, and show that it induces an isomorphism between a free group on a finite number of generators, and the group of self-quasi-isogenies of a supersingular abelian surface, respecting a principal polarization and a prime-to-p level structure. Along the way, we classify certain pro-étale torsors in terms of the pro-étale fundamental group, describe the category of geometric covers of non-normal schemes, and use this to compute pro-étale fundamental groups of curves.
DOI : 10.4171/dm/930
Classification : 14F35, 14H30, 11G10, 14K02
Mots-clés : Abelian surfaces, supersingular, pro-étale fundamental group, quasi-isogeny group 
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     author = {Thibaud van den Hove},
     title = {Quasi-isogeny groups of supersingular abelian surfaces via pro-\'etale fundamental groups},
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     doi = {10.4171/dm/930},
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Thibaud van den Hove. Quasi-isogeny groups of supersingular abelian surfaces via pro-étale fundamental groups. Documenta mathematica, Tome 28 (2023) no. 5, pp. 1053-1078. doi: 10.4171/dm/930

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