  We prove that for an endomorphism $f$ of an abelian manifold defined over an
algebraically closed field of arbitrary characteristic, $ \chi_ {2q} (f) =
\lambda_q (f) $. Note that this paper is based on recent results due to Fei Hu
\cite{Hu19}, \cite{Hu-cndd}, \cite{Hu-Tits} e Truong \cite {Truong1611}.
