Level structure, arithmetic representations, and noncommutative Siegel linearization
@article{Kadets2022LevelSA, title={Level structure, arithmetic representations, and noncommutative Siegel linearization}, author={Borys Kadets and Daniel Litt}, journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)}, year={2022}, volume={2022}, pages={219 - 238} }
Abstract Let ℓ{\ell} be a prime, k a finitely generated field of characteristic different from ℓ{\ell}, and X a smooth geometrically connected curve over k. Say a semisimple representation of π1ét(Xk¯){\pi_{1}^{{\text{\'{e}t}}}(X_{\bar{k}})} is arithmetic if it extends to a finite index subgroup of π1ét(X){\pi_{1}^{{\text{\'{e}t}}}(X)}. We show that there exists an effective constant N=N(X,ℓ){N=N(X,\ell)} such that any semisimple arithmetic representation of π1ét(Xk¯){\pi_{1}^{{\text{\'{e}t…
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