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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

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
Zbl 0595.12003
Full Text: DOI EuDML
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