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We introduce the notion of an arithmetic matroid, whose main example is givenby a list of elements of a finitely generated abelian group. In particular westudy the representability of its dual, providing an extension of the Galeduality to this setting. Guided by the geometry of generalized toricarrangements, we provide a combinatorial interpretation of the associatedarithmetic Tutte polynomial, which can be seen as a generalization of Crapo'sformula for the classical Tutte polynomial.

Arithmetic matroids, Tutte polynomial, and toric arrangements