Finitely continuous differentials on generalized power series

Abstract

Abstract Let κ[[eG]] be the field of generalized power series with exponents in a totally ordered Abelian group G and coefficients in a field κ. Given a subgroup H of G such that G/H is finitely generated, we construct a vector space ΩG/H of differentials as a universal object in certain category of κ[[eH]]-derivations on κ[[eG]]. The vector space ΩG/H together with logarithmic residues gives rise to a framework for certain combinatorial phenomena, including the inversion formula for diagonal delta sets.