# Level structure, arithmetic representations, and noncommutative Siegel linearization

@inproceedings{Kadets2021LevelSA, title={Level structure, arithmetic representations, and noncommutative Siegel linearization}, author={Borys Kadets and Daniel Litt}, year={2021} }

. Let ℓ be a prime, k a ﬁnitely generated ﬁeld of characteristic diﬀerent from ℓ , and X a smooth geometrically connected curve over k . Say a semisimple representation of π ´et1 ( X ¯ k ) is arithmetic if it extends to a ﬁnite index subgroup of π ´et1 ( X ). We show that there exists an eﬀective constant N = N ( X,ℓ ) such that any semisimple arithmetic representation of π ´et1 ( X ¯ k ) into GL n ( Z ℓ ), which is trivial mod ℓ N , is in fact trivial. This extends a previous result of the…

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