How do you prove that category of representations of $G_m$ is equivalent to the category of finite dimensional graded vector spaces?

310 Views Asked by At

$G_m$ is the multiplicative algebraic groups. I don't have much experience with dealing with this category of finite dimensional graded vector spaces, and only know the basics about what its objects look like. I'd appreciate if anyone can explain how to prove this, or cite a reference where I can look at the proof.