To be precise, the film is based on a stage play and character portrayal came from it, too. The theme of genius vs mere human can be traced back further, to Pushkin's short play "Mozart and Salieri" in 1830 [1].

But I agree that the movie is so good that many people would take it as "based on true story".

[1] https://ebooks.adelaide.edu.au/p/pushkin/aleksandr/p98mo/