The highly anticipated filmed version of the Broadway musical Hamilton debuted over the weekend to critical acclaim, currently sitting at 99% "Certified Fresh" on Rotten Tomatoes and giving Disney+ a major influx of new subscribers. Fans of the production wouldn't be too out of line to wonder what the movie's prospect of being given Oscar gold at the 2021 ceremony since this is technically a movie (it was planned to debut in theaters and even carries a rating from the Motion Picture Association). Unfortunately, none of that matters, as the film has been ruled ineligible for next year's Oscars ceremony.
The Academy of Motion Picture Arts and Sciences previously allowed filmed versions of plays to be nominated for awards, with 1965's Othello nominated for four Oscars and 1976's Give 'em Hell, Harry! nominated for one. In the years since though they've changed the rules, making a note that "Works that are essentially promotional or instructional are not eligible, nor are works that are essentially unfiltered records of performances."
AMPAS has already postponed the next Academy Awards ceremony from February 28th of next year to April 25, 2021. In addition they've extended the eligibility window from concluding on December 21 of this year until February 28 of next year.
Though this rules out an Oscar for Hamilton next year, the film could still be nominated for an Emmy according to Variety. The television academy would allow Hamilton to compete in its next batch of awards voting by submitting itself in the "Outstanding Variety Special (Pre-Recorded)" category. Per their rules, filmed performances of Broadway plays are eligible as appropriate in variety special (live) or variety special (pre-recorded). The 72nd Primetime Emmy Awards are scheduled to take place this September and only cover programming from June 1, 2019 until May 31, 2020, meaning Hamilton would have to compete in next year's ceremony.
The filmed version of Hamilton was produced in 2016 with the original Broadway cast and sat on an encrypted hard drive for a few years before finally being sold to The Walt Disney Company. Producing the film cost the creative team behind it less than $10 million according to The New York Times, a sum quickly made back after the sold the film to Disney for nearly $75 million. It's worth noting that this deal doesn't give Disney the rights to make an actual feature film adaptation of the show, something that Miranda still holds the rights to and is unsure if it will ever happen. Should that happen it would naturally be eligible for Oscars, and likely win some.