It's good, the combination of Death Note and MHA is a good crossover. However, the story could improve.
1. Stupidity:
Why DEKU of all names? Like, seriously? I can already tell how Izuku would get caught. Katsuki shouting at Izuku, "DEKU!", which so happens that ACE somehow hears it too. Then from there on, he watches Izuku closely.
Characterization:
So, AFO ordered Tomura to stalk Izuku. But when revealed that Izuku didn't know AFO, it made Tomura look at Izuku as an ignorant dobe.
However, AFO? Nah, the guy would smell suspicions from Izuku a mile away. Why? It's because Izuku is a Hero/Villain fanboy! HOW can he not know AFO? Either he has to be the worst fanboy or like I said, suspicious.
And do you seriously think AFO doesn't have a lie detector quirk? He made his empire through blood and deceit, and you think a kid who decided to change weeks later has some god-level acting skills?
Nah bro, you got to make the transition properly, everything seems... fast.
3. Speech
Things get weird after people start talking. It's because, you merely put "...." the quotation marks. You don't add details to who is talking, how they express themselves when talking, and many more.
4. Background:
Who tf is ACE? Who tf is ROOK? What does All Might and other Heroes opinion on the goings of these incidents?
You simply said ACE was able to figure out AFO's other identity, which is good. But it doesn't paint ACE as some God detective like L is.
Adding perspective of others will help the story, especially All Might's view. He is the number one Hero, and his view will make things interesting.
That's all for now, but I look forward to your work!