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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
Zbl 0595.12003
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