Auteurs : Salvatore Floccari

We prove that the rational Chow motive of a six dimensional hyper-Kähler variety obtained as symplectic resolution of O'Grady type of a singular moduli space of semistable sheaves on an abelian surface $A$ belongs to the tensor category of motives generated by the motive of $A$. We in fact give a formula for the rational Chow motive of such a variety in terms of that of the surface.
As a consequence, the conjectures of Hodge and Tate hold for many hyper-Kähler varieties of OG6-type.

Comment: 10 pages; final version, published in EPIGA

• 14C15 - (Equivariant) Chow groups and rings; motives
• 14C30 - Transcendental methods, Hodge theory (algebro-geometric aspects)
• 14D20 - Algebraic moduli problems, moduli of vector bundles
• 14J42 - Holomorphic symplectic varieties, hyper-Kähler varieties

• 1 zbMATH Open