• Corpus ID: 227127525

# Absolute Hodge and $\ell$-adic Monodromy

@article{Urbanik2020AbsoluteHA,
title={Absolute Hodge and \$\ell\$-adic Monodromy},
author={David Urbanik},
journal={arXiv: Algebraic Geometry},
year={2020}
}
• 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 $\mathbb{V}_{s_… ## References SHOWING 1-9 OF 9 REFERENCES Hodge loci and absolute Hodge classes This paper addresses several questions related to the Hodge conjecture. First of all we consider the question, asked by Maillot and Soule, whether the Hodge conjecture can be reduced to the case of o-minimal GAGA and a conjecture of Griffiths • Mathematics • 2018 We prove a conjecture of Griffiths on the quasi-projectivity of images of period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop a theory of analytic Period Mappings and Period Domains • Mathematics • 2017 Part I. Basic Theory of the Period Map: 1. Introductory examples 2. Cohomology of compact Kahler manifolds 3. Holomorphic invariants and cohomology 4. Cohomology of manifolds varying in a family 5. Notes on absolute Hodge classes • Mathematics • 2011 We survey the theory of absolute Hodge classes. The notes include a full proof of Deligne's theorem on absolute Hodge classes on abelian varieties as well as a discussion of other topics, such as the Hodge Cycles on Abelian Varieties The main result proved in these notes is that any Hodge cycle on an abelian variety (in characteristic zero) is an absolute Hodge cycle — see §2 for definitions and (2.11) for a precise statement of On the de rham cohomology of algebraic varieties © Publications mathématiques de l’I.H.É.S., 1966, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// Fundamental Groups and Path Lifting for Algebraic Varieties We study 3 basic questions about fundamental groups of algebraic varieties. For a morphism, is being surjective on$\pi_1\$ preserved by base change? What is the connection between openness in the
Théorie de Hodge, II
A filter, especially for swimming pools, comprises a group of superposed filter beds operating in parallel within a single outer casing. By this means, the capacity of the filter for the floor area