The fundamental theorem of dimension theory in commutative algebra states that given a module $M$ over a noetherian local ring $A$, we have $s(M)=\text{dim}(M)=d(M)$ (where $s(M)$ is the infimum of integers $k$ such that there exists $x_1...x_k$ such that $M/(x_1...x_k)M$ is of finite length, and $d(M)$ is the degree of the Samuel polynomial of $M$)

I know about the standard proof as is written down in Serre's *Local Algebra*, or in the book *Homological Methods for Commutative Algebra* [S. Raghavan, R. Balwant Singh, R. Sridharan]
(side question: what are other good references for the dim. theorem? Please add details).

**Question**

I was wondering if there exists some slick / more conceptual proof by applying some more technology, maybe using homological algebra or algebraic geometric methods, or whatever.