Albanese and Picard 1-motives, by L. Barbieri Viale and V. Srinivas

We define, in a purely algebraic way, 1-motives Alb+(X), Alb-(X), Pic+(X) and Pic-(X) associated with any algebraic scheme X over an algebraically closed field of characteristic zero. For X over complex numbers of dimension n the Hodge realizations are, respectively, H^{2n-1}(X)(n), H_{1}(X), H^{1}(X)(1) and H_{2n-1}(X)(1-n).

L. Barbieri Viale <>
V. Srinivas <>