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arxiv: math/9803112 · v1 · submitted 1998-03-24 · 🧮 math.AG

Albanese and Picard 1-motives

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keywords algebraicmotivesalbanesealgebraicallyassociatedcharacteristiccloseddefine
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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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