Summary
We propose a new way to describe, universally, thel-adic Galois representations associated to each “almost pro-l” tower of etale coverings ofP 1\{0, 1, ∞}. This generalizes our universal power series for Jacobi sums (cf. [I]) which arises from the tower of Fermat curves of degreel n (n→∞), and contains the case of the tower of modular curves of level 2ml n (m: fixed,n→∞) as another important special case. As a fundamental tool, we shall establish and use an “almost pro-l version” of the theorems of Blanchfield and of Lyndon in Fox free differential calculus.
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Ihara, Y. On Galois representations arising from towers of coverings of P1\{0, 1, ∞}. Invent Math 86, 427–459 (1986). https://doi.org/10.1007/BF01389262
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DOI: https://doi.org/10.1007/BF01389262