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jeunes en arithmétique et variétés algébriques
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Participants must travel to Nîmes at their own expense; no financial support is provided for the trip. The trip from Nîmes to Maison Clément, as well as on-site expenses, will be covered by the organizers. We warmly suggest you to arrive on Sunday 14 June and leave on Friday 19 June.

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1. The Hodge conjecture for abelian varieties
2. Abelian varieties of Weil type
3. Mumford-Tate groups
4. Schoen's proof of the algebraicity of the Weil classes on abelian fourfolds of Weil type, case of $\mathbb{Q}(\sqrt{-3})$
5. Semiregularity and deformations
6. The semiregularity theorem and its generalization to twisted sheaves
7. The Clifford algebra and the spin group associated to an abelian variety
8. Polarized abelian varieties of Weil type from $K$-secants
9. Equivalences of derived categories of coherent sheaves
10. Chevalley's isomorphism and Orlov's derived equivalence
11. Hodge Weil classes on $X\times\hat{X}$ from tensor squares of pure spinors
12. Semiregular secant sheaves on abelian $3$-folds
13. An object $E$ of $D^b(X\times \hat{X})$ with a $\operatorname{Spin}(V)_P$-invariant $\kappa(E)$ and a $9$ dimensional $\ker(ob_E)=\ker(\rfloor ch_E)$
14. A $[\mathbb{Z}/(d+1)\mathbb{Z}]^2$-equivariant sheaf over $X\times \hat{X}$
15. The $CM$-fields case

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