Here's the `posts.py` file with Pydantic schemas for posts, located in the `app/api/v1/schemas/` directory:

from typing import Optional
from pydantic import BaseModel
from datetime import datetime

class PostBase(BaseModel):
    title: str
    content: str

class PostCreate(PostBase):
    pass

class PostUpdate(PostBase):
    pass

class PostInDBBase(PostBase):
    id: int
    created_at: datetime
    updated_at: Optional[datetime] = None

    class Config:
        orm_mode = True

class Post(PostInDBBase):
    pass

class PostList(BaseModel):
    __root__: list[Post]

Explanation:

1. We import the necessary modules: `typing` for type annotations, `pydantic` for defining data models, and `datetime` for working with date and time objects.

2. `PostBase` is a Pydantic model that defines the base fields for a post: `title` and `content`.



5. `PostInDBBase` inherits from `PostBase` and adds additional fields: `id`, `created_at`, and `updated_at`. The `orm_mode` config is set to `True` to allow Pydantic to read data from SQLAlchemy models.