How to evaluate meromorphic germs at their poles while preserving a
locality principle reminiscent of locality in QFT is a question that lies
at the heart of pQFT. It further arises in other disguises in number
theory, the combinatorics on cones and toric geometry. We introduce an
abstract notion of locality and a related notion of mutually independent
meromorphic germs. The question then amounts to extending the ordinary
evaluation at a point on holomorphic germs to certain algebras of
meromorphic germs, in such a way that the extension factorises on mutually
In the talk, we shall describe a family of such extended evaluators on germs
of meromorphic germs in several variables with a prescribed type of
(linear) poles and show that modulo a Galois type transformation, they
amount to a minimal subtraction scheme in several variables.
This talk is based on joint work with Li Guo and Bin Zhang.