The action of SL(2) on abelian varieties

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

We show that the algebraic group SL(2) acts on any polarized abelian variety
A through correspondences. As a consequence we recover the action of SL(2) on
the Chow group CH(A) (with rational coefficients), and this gives rise to
Lefschetz type properties for algebraic cycles on A .

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