Albanese and Picard 1-motives

Details Albanese and Picard 1-motives Albanese and Picard 1-motives

1998-03-24

arxiv.org/abs/math/9803112v1

C.R.Acad.Sci.Paris 326 (1998) 1397-1401

Mathematics

Algebraic Geometry

5 pages, LaTeX, submitted as CR Note

Scientific paper

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 $\C$ of
dimension $n$ the Hodge realizations are, respectively, $H^{2n-1}(X)(n)$,
$H_{1}(X)$, $H^{1}(X)(1)$ and $H_{2n-1}(X)(1-n)$.

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