Arithmetic representations of fundamental groups I

  title={Arithmetic representations of fundamental groups I},
  author={Daniel Litt},
  journal={Inventiones mathematicae},
  • Daniel Litt
  • Published 22 August 2017
  • Mathematics
  • Inventiones mathematicae
Let X be a normal algebraic variety over a finitely generated field k of characteristic zero, and let $$\ell $$ℓ be a prime. Say that a continuous $$\ell $$ℓ-adic representation $$\rho $$ρ of $$\pi _1^{\acute{\mathrm{e}}\text {t}}(X_{\bar{k}})$$π1e´t(Xk¯) is arithmetic if there exists a finite extension $$k'$$k′ of k, and a representation $$\tilde{\rho }$$ρ~ of $$\pi _1^{\acute{\mathrm{e}}\text {t}}(X_{k'})$$π1e´t(Xk′), with $$\rho $$ρ a subquotient of $$\tilde{\rho }|_{\pi _1(X_{\bar{k… 
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