How to verify JWT from AWS Cognito in the API backend?

I'm building a system consisting of an Angular2 single page app and a REST API running on ECS. The API runs on .Net/Nancy, but that might well change.

I would like to give Cognito a try and this is how I imagined the authentication workflow:

1. SPA signs in user and receives a JWT
2. SPA sends JWT to REST API with every request
3. REST API verfies that the JWT is authentic

My question is about step 3. How can my server (or rather: my stateless, auto-scaled, load-balanced Docker containers) verify that the token is authentic? Since the "server" hasn't issued the JWT itself, it can't use its own secret (as described in the basic JWT example here).

I have read through the Cognito docs and googled a lot, but I can't find any good guideline about what to do with the JWT on the server side.