build hopes on
build (one's) hopes on (someone or something)
To have expectations that are tied to the success, performance, etc., of a particular person or thing. Why are we building our hopes on him when we know he's not popular enough to defeat the incumbent? I had built my hopes on this promotion and was crushed when I didn't get it.
build one's hopes on someone or something
to make plans or have aspirations based on someone or something. I have built my hopes on making a success of this business. I built my hopes on John's presidency.