• Corpus ID: 227127525

Absolute Hodge and $\ell$-adic Monodromy

  title={Absolute Hodge and \$\ell\$-adic Monodromy},
  author={David Urbanik},
  journal={arXiv: Algebraic Geometry},
  • D. Urbanik
  • Published 21 November 2020
  • Mathematics
  • arXiv: Algebraic Geometry
Let $\mathbb{V}$ be a motivic variation of Hodge structure on a $K$-variety $S$, let $\mathcal{H}$ be the associated $K$-algebraic Hodge bundle, and let $\sigma \in \textrm{Aut}(\mathbb{C}/K)$ be an automorphism. The absolute Hodge conjecture predicts that given a Hodge vector $v \in \mathcal{H}_{\mathbb{C}, s}$ above $s \in S(\mathbb{C})$ which lies inside $\mathbb{V}_{s}$, the conjugate vector $v_{\sigma} \in \mathcal{H}_{\mathbb{C}, s_{\sigma}}$ is Hodge and lies inside $\mathbb{V}_{s_… 


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