For which film did Heath Ledger win the Oscar for Best Supporting Actor?

For which film did Alan Arkin win the Oscar for Best Supporting Actor? Who won the Oscar for Best Supporting Actor for 'No Country for Old Men'? For which film did Javier Bardem win the Oscar for Best Supporting Actor? Who won the Oscar for Best Supporting Actor for 'The Dark Knight'? Who won the Oscar for Best Supporting Actor for 'Inglourious Basterds'? Who won the Oscar for Best Supporting Actor for 'The Fighter'? For which film did Christian Bale win the Oscar for Best Supporting Actor? Who won the Oscar for Best Supporting Actor for 'Beginners'?