Death Note Pilot (2003)

Taro Kagami has a hard time at school: He is often harassed and beaten up by his classmates. But his life changes significantly as he happens to find a black notebook with the inscription “Death Note”: Now Taro is haunted by the former owner of the Death Note, a shinigami called Ryuk. The grotesque creature tells Taro that any person whose name is written in the Death Note will die. Unluckily Taro has already used the notebook as a diary and mentioned some of his bullies in the entries. When he goes to school again, his class is told by his teacher that some students died for an unknown reason. As if that wasn’t enough, the police is searching for suspects. And Taro is one of them . . .

Source: www.anisearch.com/manga/10748