Geodesic
On Motivic Realizations of the Canonical Hermitian Variations of Hodge Structure of Calabi–Yau Type over type $D^{\mathbb{H}}$ Domains
Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 209-221

Voir la notice de l'article provenant de la source Cambridge University Press

Let ${\mathcal{D}}$ be the irreducible Hermitian symmetric domain of type $D_{2n}^{\mathbb{H}}$. There exists a canonical Hermitian variation of real Hodge structure ${\mathcal{V}}_{\mathbb{R}}$ of Calabi–Yau type over ${\mathcal{D}}$. This short note concerns the problem of giving motivic realizations for ${\mathcal{V}}_{\mathbb{R}}$. Namely, we specify a descent of ${\mathcal{V}}_{\mathbb{R}}$ from $\mathbb{R}$ to $\mathbb{Q}$ and ask whether the $\mathbb{Q}$-descent of ${\mathcal{V}}_{\mathbb{R}}$ can be realized as sub-variation of rational Hodge structure of those coming from families of algebraic varieties. When $n=2$, we give a motivic realization for ${\mathcal{V}}_{\mathbb{R}}$. When $n\geqslant 3$, we show that the unique irreducible factor of Calabi–Yau type in $\text{Sym}^{2}{\mathcal{V}}_{\mathbb{R}}$ can be realized motivically.
DOI : 10.4153/CMB-2017-083-5
Mots-clés : variations of Hodge structure, Hermitian symmetric domain 
Zhang, Zheng. On Motivic Realizations of the Canonical Hermitian Variations of Hodge Structure of Calabi–Yau Type over type $D^{\mathbb{H}}$ Domains. Canadian mathematical bulletin, Tome 62 (2019) no. 1, pp. 209-221. doi: 10.4153/CMB-2017-083-5
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     journal = {Canadian mathematical bulletin},
     pages = {209--221},
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     volume = {62},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-083-5/}
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