以下に実装例を示す：

```
python

from fastapi import FastAPI

app = FastAPI()

@app.get("/")
async def root():
    return {"message": "<h1>Hello, world!</h1>"}
```

Python環境でコードを実行し、ウェブ・ブラウザでhttp://localhost:8000。
Here's an example implementation:

```
python

from fastapi import FastAPI

app = FastAPI()

@app.get("/")
async def root():
    return {"message": "<h1>Hello, world!</h1>"}
```

You can run this server by executing the code in a Python environment and then visiting http://localhost:8000 in your web browser.