Let $\varphi:X^{\prime}\rightarrow X$ be a proper morphism of algebraic varieties over $K$. Then there is a linear map $\varphi_{*}:D_{p,q}((X^{\prime})^{\rm an})\rightarrow D_{p,q}({X^{\rm an}})$, where the push-forward $\varphi_{*}(T^{\prime})\in D_{p,q}({X^{\rm an}})$ of $T^{\prime}\in D_{p,q}((X^{\prime})^{\rm an})$ is characterized by

$$\varphi_{*}(T^{\prime})(\alpha)=T^{\prime}(\varphi^{*}(\alpha))$$

for every $\alpha\in A_{c}^{p,q}({X^{\rm an}})$. It follows from continuity of the map $\varphi^{*}:A_{c}^{p,q}({X^{\rm an}}))\rightarrow A_{c}^{p,q}((X^{\prime})^{\rm an})$ that $\varphi_{*}(T)$ is indeed a current on $T$. To define the push-forward, we need the fact that a proper algebraic morphism induces a proper morphism between the analytifications meaning that the preimage of a compact subset in ${X^{\rm an}}$ is compact (see [Be90], Proposition 3.4.7).