It's the distant future. Crime has been eliminated due to the development of the "general solution" by the famous mathematician Daria Epsilon. Citizens live in peace and luxury. However one day a body is discovered, there has been a murder! Widespread panic ensues as the citizens realise there is nobody left who can solve the case. Luckily the famous detective Rodger Stevens has been kept in cryogenic storage in case crime ever returned. Now the hard boiled detective, with the help of Daria Epsilon, must solve the murder in a strange new world and discover why the general solution has failed.

Obviously you can change names, genders whatever. Another idea is that the person who is killed is the mathematician who discovered the general solution. OR that the person who did the killing was the architect of the general solution who is now this crazy old hermit and the "helper" is just someone from the times assigned to help the detective get used to modern times.

Also, you could possibly have fun that the detective is from the 1940s and is all wonderfully out of place. Because fish out of temporal water is the funnest trope. Or the whole world could be 1940s ish.

(This was in no way slightly inspired by Captain America. IN NO WAY)