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We develop a theory of Tannakian Galois groups for t-motives and relate thisto the theory of Frobenius semilinear difference equations. We show that thetranscendence degree of the period matrix associated to a given t-motive isequal to the dimension of its Galois group. Using this result we prove thatCarlitz logarithms of algebraic functions that are linearly independent overthe rational function field are algebraically independent.Comment: 39 page

Tannakian duality for Anderson–Drinfeld motives and algebraic independence of Carlitz logarithms