Manga by author Takeuchi Ryousuke

The story of Sherlock Holmes, reimagined with Moriarty as the protagonist and exploring his motivation in becoming the greatest criminal Britain has ever seen.

From MangaHelpers: The world is in a war against an alien race called "Mimics," who have taken over most of the world with a mission to eliminate the human race. Keiji Kiriya is a new recruit in the United Defense Force, which is battling against these "Mimics." On his first day of deployment, Keiji and his unit encounter "Mimics" and are all killed... Or was it all a dream? For some inexplicable reason, after every time he dies, he is resurrected and returned back to the day before the battle. Why does this happen to Keiji and how can he escape from this never ending cycle?

.The story of Sherlock Holmes, reimagined with Moriarty as the protagonist and exploring his motivation in becoming the greatest criminal Britain has ever seen.