points of the Albanese variety of X coincide. Replacing the Chow group by Suslin–Voevodsky algebraic singular homology after the introduction of Motivic cohomology Roitman's theorem has been obtained and reformulated in the motivic framework. For example, a similar result holds for non-singular quasi-projective varieties. Further versions of Roitman's theorem are available for normal schemes. Actually, the most general formulations of Roitman's theorem (i.e. homological, cohomological, and Borel–Moore) involve the motivic Albanese complex and have been proven by Luca Barbieri-Viale and Bruno Kahn (see the references III.13). Connection to Picard variety The Albanese variety is dual to the Picard variety (the connected component of zero of the Picard scheme classifying invertible sheaves on V): For algebraic curves, the Abel–Jacobi theorem implies that the Albanese and Picard varieties are isomorphic. See also Intermediate Jacobian Albanese scheme Motivic Albanese Notes & references Abelian varieties