We work out properties of smooth projective varieties X over a (not necessarily algebraically closed) field $\textit{k}$ that admit collections of objects in the bounded derived category of coherent sheaves D$^{b}$(X) that ...

We show that the motive of the Hilbert scheme of length-n subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, ...

Using a codimension-1 algebraic cycle obtained from the Poincar e line bundle, Beauville de ned the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition ...