{"id":"hexagon/2610.00662","pdf":"https://hexagonmath.org/pdf/2610.00662v1","url":"https://hexagonmath.org/abs/2610.00662v1","tags":["math.NT","msc:14C25","msc:14F30","msc:14K15","msc:14G35","msc:14L05","Dieudonne modules","Mumford fourfolds","Shimura varieties","Weil classes"],"score":0,"title":"Integral crystalline Tate classes of codimension two at supersingular points of Mumford's fourfolds","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Antti Hippeläinen"],"reviews":0,"subject":"math.AG","summary":"For a supersingular abelian variety $X$ over $\\bar{\\mathbb{F}}_p$, let $T^4(X)$ be the lattice of integral crystalline Tate classes of codimension $2$ and $S(X)$ the span of products of divisor classes. Let $p\\ge5$ and $\\mathscr{G}_p$ be the $p$-divisible group of the supersingular points of Mumford's families of abelian fourfolds at primes inert in their cubic field, for the hyperspecial levels given by tensor-induced lattices. For every abelian fourfold $X$ with $X[p^\\infty]\\cong\\mathscr{G}_p$ we show that $T^4(X)/S(X)\\cong(\\mathbb{Z}/p)^4$, and that the integral crystalline Tate…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Python"],"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}