On the Hilbert-Samuel multiplicity of Fredholm tuples Jorg Eschmeier 47A1347A5313D4032C35multivariable operator theoryHilbert-Samuel multiplicityFredholm tuplesstabilized cohomology dimensions For commuting tuples $R \in L(Z)^n$ of Banach-space operators that arise as quotients of lower semi-Fredholm systems $T$ with constant cohomology dimension $\dim H^n(z-T, X)$ near the origin $0 \in \mathbb{C}^n$, we show that the Hilbert-Samuel multiplicity of $R$ calculates the rank of the cohomology sheaf $\mathcal{H}^n(z-R, \mathcal{O}^Z_{\mathbb{C}^n})$ at $z = 0$. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2930 10.1512/iumj.2007.56.2930 en Indiana Univ. Math. J. 56 (2007) 1463 - 1478 state-of-the-art mathematics http://iumj.org/access/