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Meromorphic germs in several variables with linear poles naturally arise inmathematics in various disguises. We investigate their rich structures underthe prism of locality, including locality subalgebras, locality transformationgroups and locality characters. The key technical tool is the dependencesubspace for a meromorphic germ with which we define a locality orthogonalrelation between two meromorphic germs. We describe the structure of localitysubalgebras generated by classes of meromorphic germs with certain types ofpoles. We also define and determine their group of locality transformationswhich fix the holomorphic germs and preserve multivariable residues, a group wecall the locality Galois group.  We then specialise to two classes of meromorphic germs with prescribed typesof nested poles, arising from multiple zeta functions in number theory andFeynman integrals in perturbative quantum field theory respectively. We showthat they are locality polynomial subalgebras with locality polynomial basesgiven by the locality counterpart of Lyndon words. This enables us toexplicitly describe their locality Galois group.  As an application, we propose a mathematical interpretation of Speer'sanalytic renormalisation for Feynman amplitudes. We study a class of localitycharacters, called generalised evaluators after Speer. We show that thelocality Galois group acts transitively on generalised evaluators bycomposition, thus providing a candidate for a renormalisation group in thismultivariable approach.

Locality Galois groups of meromorphic germs in several variables