{"id":"hexagon/2610.00686","pdf":"https://hexagonmath.org/pdf/2610.00686v1","url":"https://hexagonmath.org/abs/2610.00686v1","tags":["math.AG","msc:11G09","msc:11R58","Anderson t-motives","Drinfeld modules","function fields","uniformizability"],"score":0,"title":"Uniformizability of elementary Anderson $t$-motives of dimension $2$","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.NT","summary":"Let $M(A)$, $A\\in M_2(\\mathbb{C}_\\infty)$, be the elementary Anderson $t$-motive of dimension $2$ and rank $4$ defined by $Te=\\theta e+A\\tau e+\\tau^2e$. Using the affine equation of Ehbauer, Grishkov and Logachev, we give an explicit sufficient condition for $M(A)$ to be uniformizable, in terms of the valuations of the coefficients of that equation. It holds as soon as no cancellation occurs among the four summands of one of these coefficients; in particular $h^1(M(A))=4$ in the simple case where no cancellation occurs in any coefficient. This proves their Conjecture 3.7: $h^1(M(A))=4$…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}