论文标题
$ h^1 $的某些安德森T-动力的计算
Calculation of $h^1$ of some Anderson t-motives
论文作者
论文摘要
我们考虑了Anderson T-Motives $ M $ dimension 2和等级4由一些简单的显式方程定义为$ 2 \ times2 $矩阵。我们使用$ h^1（m）$的显式计算方法 - 其同胞组$ h^1（m）$的维度（=我们较早的论文中其双t- t-Motive $ m'$的晶格的尺寸。我们计算$ h^1（m）$的$ m $ $ $ $，由对角上的所有矩阵和其他一些矩阵定义。这些方法允许对大多数（可能全部）T-动物进行类似的计算。所有Anderson T-Motives $ M $的$ H^1 $都在考虑不平等$ h^1（m）\ le4 $，而在所有已知示例中，我们都有$ h^1（m）= 0,1,4 $。存在$ h^1 = 2,3 $的这种类型的$ m $吗？我们不知道，这是进一步研究的主题。
We consider Anderson t-motives $M$ of dimension 2 and rank 4 defined by some simple explicit equations parameterized by $2\times2$ matrices. We use methods of explicit calculation of $h^1(M)$ -- the dimension of their cohomology group $H^1(M)$ ( = the dimension of the lattice of their dual t-motive $M'$) developed in our earlier paper. We calculate $h^1(M)$ 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. $h^1$ of all Anderson t-motives $M$ under consideration satisfy the inequality $h^1(M)\le4$, while in all known examples we have $h^1(M)=0,1,4$. Do exist $M$ of this type having $h^1=2,3$? We do not know, this is a subject of further research.
