Tannakian duality for Anderson–Drinfeld motives and algebraic independence of Carlitz logarithms
Tannakian duality for Anderson–Drinfeld motives and algebraic independence of Carlitz logarithms
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DOI：
10.1007/s00222-007-0073-y
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发表时间：
2005-06
影响因子：
3.1
通讯作者：
M. Papanikolas
中科院分区：
文献类型：
--
作者：
M. Papanikolas
我们发展了 Tannakian Galois 群的动机理论，并将其与 Frobenius 半线性差分方程的理论联系起来。我们证明，与给定动机相关的周期矩阵的超越度等于其伽罗瓦群的维数。利用这个结果，我们证明了在有理函数域上线性无关的代数函数的 Carlitz 对数是代数无关的。
We develop a theory of Tannakian Galois groups fort-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a givent-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.