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The weight $w$ of the Sato-Tate group $G$ of a motive $X$ is determined by the cohomology group $H^w(X,\mathbb{Q}_\ell)$ used to define $G$. For a prime of norm $q$, the characteristic polynomial of Frobenius is a Weil $q^w$-polynomial.

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  • Review status: reviewed
  • Last edited by Kiran S. Kedlaya on 2018-06-20 04:06:06.206000