2020/05/30 by Ehbauer, Stefan, Grishkov, Aleksandr, Logachev, Dmitry
#11G09 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2006.00316
We consider Anderson t-motives M of dimension 2 and rank 4 defined by some simple explicit equations parameterized by 2×2 matrices. We use methods of explicit calculation of h1(M) -- the dimension of their cohomology group H1(M) ( = the dimension of the lattice of their dual t-motive M') developed in our earlier paper. We calculate h1(M) for M defined by all matrices having 0 on the diagonal, and by some other matrices. These methods permit to make analogous calculations for most (probably all) t-motives. h1 of all Anderson t-motives M under consideration satisfy the inequality h1(M)≤4, while in all known examples we have h1(M)=0,1,4. Do exist M of this type having h1=2,3? We do not know, this is a subject of further research.