Given a K3 surface $X$, the cup product defines a non-degenerate even unimodular structure on the lattice $H^2(X,\mathbb{Z})$. Inside this lattice we have the Neron-Severi group $\text{NS}(X)$, which is also a primitive lattice. The rank of $\text{NS}(X)$, denoted by $\rho(X)$, is called the Picard number of $X$. The orthogonal complement of $\text{NS}(X)$ is by definition the transcendental lattice \begin{equation} T(X):=\text{NS}(X)^\perp \subset H^2(X,\mathbb{Z}). \end{equation}

In the note "Arithmetic of K3 surfaces" by Matthias Schutt, the author says that

"If $X$ is defined over some number field, the lattices of algebraic and transcendental cycles give rise to Galois representations of dimension $\rho(X)$ resp. $22-\rho(X)$."

Does he mean that the Galois representation arise from the etale cohomology $H^2_{et}(X,\mathbb{Q}_\ell)$ splits into the direct sum of two sub-representations with dimension $\rho(X)$ (associated to the algebraic cycles) and $22-\rho(X)$ (associated to the transcendental cycles)?

I guess this statement might be true generally for algebraic surfaces. Could anyone explain it more carefully, and give a reference if possible?

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