2018/07/23 by Aleksandr Grishkov, Grishkov, Aleksandr, Dmitry Logachev +1
Computer Science · Mathematics · #11G09 #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1807.08675
openalex publication_date 2018/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be an Anderson t-motive of dimension n and rank r. Associated are two \Bbb Fq[T]-modules H1(M), H1(M) of dimensions h1(M), h1(M)≤ r - analogs of H1(A,\Bbb Z), H1(A,\Bbb Z) for an abelian variety A. There is a theorem (Anderson): h1(M)=r \iff h1(M)=r; in this case M is called uniformizable. It is natural to expect that always h1(M)=h1(M). Nevertheless, we explicitly construct a counterexample. Further, we answer a question of D.Goss: is it possible that two Anderson t-motives that differ only by a nilpotent operator N are of different uniformizability type, i.e. one of them is uniformizable and other not? We give an explicit example that this is possible.