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We investigate properties of essential spectra of disjointness preservingoperators acting on Banach $C(K)$-modules. In particular, we prove that undersome very mild conditions the upper semi-Fredholm spectrum of such an operatoris rotation invariant. In the last part of the paper we provide a fulldescription of the spectrum and the essential spectra of operators acting onKaplansky modules of the form $T = wU$, where $w \in C(K)$, $U$ is a$d$-isomorphism, and the spectrum of $U$ is a subset of the unit circle.

Spectrum of Weighted Composition Operators Part VI Essential spectra of $d$-endomorphisms of Banach $C(K)$-modules