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On Galois representations arising from towers of coverings of \(\mathbb P^1\backslash \{0,1,\infty \}\). (English) Zbl 0585.14020
A new way is proposed to describe, universally, the \(\ell\)-adic Galois representations associated to each “almost pro-\(\ell\) tower” of étale coverings of \(\mathbb P^1\setminus \{0,1,\infty \}\). This generalizes the universal power series for Jacobi sums which arises from the tower of Fermat curves of degree \(\ell^ n\) \((n\to \infty)\) [cf. the preceding work of the author in Ann. Math. (2) 123, 43–106 (1986; Zbl 0595.12003)], and contains the case of the tower of modular curves of level \(2m\ell^ n\) (\(m\) fixed, \(n\to \infty)\) as another typical special case. As a fundamental tool, an “almost pro-\(\ell\) version” of the theorems of Blanchfield and of Lyndon in Fox’s free differential calculus is established and used.
Reviewer: Yasutaka Ihara

MSC:
14H30 Coverings of curves, fundamental group
14G32 Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
11G20 Curves over finite and local fields
11R39 Langlands-Weil conjectures, nonabelian class field theory
Citations:
Zbl 0595.12003
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References:
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