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

result on hilbert polynomials of graded modules.

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

Riemann-Roch.

Clifford's theorem.

Chevalley's theorem.

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