The vanishing conjecture for the Gamma filtration on an abelian variety

Let $A$ be an abelian variety of dimension $g$, let $K=K_0(A)\otimes\mathbf Q$, and let $\operatorname{Fil}^r_\Gamma$ be the gamma filtration associated with the composed lambda-ring structure introduced in the paper. Gamma-filtration vanishing conjecture.

$$\operatorname{Fil}^{g+1}_\Gamma=0.$$

This vanishing is used in the paper as a formulation related to Beauville's conjecture and is proved there as a proposition, so it is recorded as solved rather than as an open conjecture.