Sections of a differential spectrum and factorization-free computations

Abstract

We construct sections of a differential spectrum using only localization and projective limits. For this purpose we introduce a special form of multiplicative systems generated by one differential polynomial and call it D-localization. Owing to this technique one can construct sections of a differential spectrum of a differential ring \(\mathcal{R}\) without computation of diffspec \(\mathcal{R}\). We compare our construction with Kovacic’s structure sheaf and with the results obtained by Keigher [J. Pure Appl. Algebra, 27, 163–172 (1983)]. We show how to compute sections of factor-rings of rings of differential polynomials. All computations in this paper are factorization-free.