The Stacks project

Exercise 111.56.2 (Results). State something formally equivalent to the fact discussed in the course.

1. result on hilbert polynomials of graded modules.

2. dimension of a Noetherian local ring $(R, \mathfrak m)$ and $\bigoplus _{n \geq 0} \mathfrak m^ n/\mathfrak m^{n + 1}$.

3. Riemann-Roch.

4. Clifford's theorem.

5. Chevalley's theorem.