derivative work -- you don't have the legal power to dedicate it to the public. Only the copyright owner (either the movie company or the initial author) can dedicate the work to the public domain.
Does your book infringe? Possibly. You probably remember when a Swedish author was prohibited from publishing a sequel to Catcher in the Rye (even though the lead character's name -- Holden Caulfield -- never appeared in the "sequel.") We could point to other cases as well but the takeaway is that any success you may achieve will be short-lived because it's likely that once the author or movie company learn of your work, they'll try to shut it down (and you probably can't afford to fight over it). On the other hand, if the book stays low on the radar -- for example, it's posted on a fanfiction type site -- the owners may consider it "non-threatening" and allow it to remain posted in obscurity. Because your work overlaps with fanfic, you should check out the Chilling Effects FAQs on the topic.