A lefschetz decomposition for chow motives of abelian schemes

Décomposition de motifs abéliens

“…Le Théorème 1.1 est un raffinement du résultat de Künnemann [Kün93] (A r , F )), grâce à la théorie classique des invariants [Wey97]. La surjectivité (respectivement l'injectivité) est obtenue en relevant chaque générateur (respectivement chaque relation).…”

Lie symmetries of the Chow group of a Jacobian and the tautological subring

“…The restriction m + n ≥ 2 that we imposed for our generators X m,n corresponds to considering the subalgebra of vector fields vanishing at the origin. Also, note that the operators (X 2,0 /2, X 1,1 , X 0,2 /2) generate the well known action of sl 2 on CH(J) Q (see [9]). …”

Relations between tautological cycles on Jacobians

“…By the work of Künnemann in [13], the Chow motive of J has a Lefschetz decomposition. This gives rise to an action of sl 2 on CH.J /.…”

“…In general this is known only for i 2 f0; 1; g 2; g 1; gg. Over finite fields or the algebraic closure of a finite field Beauville's conjecture is known; see Künnemann [13], Sections 7 and 8.…”