Stacks of algebras and their homology
For any increasing function $f: {\Bbb N} \rightarrow {\Bbb N}_{\ge 2}$ which takes only finitely many distinct values, a connected finite dimensional algebra $Λ$ is constructed, with the property that $\text{fin.dim}_n\, Λ= f(n)$ for all $n$; here $\text{fin.dim}_n\, Λ$ is the $n$-generated finitistic dimension of $Λ$. The stacking technique developed for this construction of homological examples permits strong control over the higher syzygies of $Λ$-modules in terms of the algebras serving as layers.
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