Let $k \subseteq \bar{k}$ be an extension of fields (Orlov in the reference below seems to indicate the same thing will hold for faithfully flat maps but the case of fields is enough for me).
On page 24 of https://arxiv.org/pdf/1402.7364.pdf, Orlov makes the following claim:
Let $A$ be a dg-category over $k$ and $M$ a dg-module over $A$. If $M \otimes_k \bar{k}$ is perfect over $A\otimes_k \bar{k}$, then $M$ is perfect over $A$.
How does one prove this? The simpler/"low-tech" the explanation, the better!
