The action of SL(2) on abelian varieties

TL;DR

This paper demonstrates that SL(2) acts on polarized abelian varieties via correspondences, leading to Lefschetz-type properties for algebraic cycles and recovering its action on the Chow group.

Contribution

It introduces a new action of SL(2) on polarized abelian varieties through correspondences, revealing Lefschetz properties for algebraic cycles.

Findings

SL(2) acts on any polarized abelian variety via correspondences

The action induces Lefschetz type properties for algebraic cycles

Recovering SL(2) action on the Chow group with rational coefficients

Abstract

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 .