Albanese and Picard 1-motives

Abstract

We define, in a purely algebraic way, 1-motives $Al{b}^{+}(X)$, $Al{b}^{-}(X)$, $Pi{c}^{+}(X)$ and $Pi{c}^{-}(X)$ associated with any algebraic scheme $X$ over an algebraically closed field of characteristic zero. For $X$ over $\C$ of dimension $n$ the Hodge realizations are, respectively, $H^{2n-1}(X)(n)$, $H_1(X)$, $H^1(X)(1)$ and $H_{2n-1}(X)(1-n)$.

5 pages, LaTeX, submitted as CR Note