Global sections of structure sheaves of Keigher rings

TL;DR

This paper proves that for Keigher rings, the differential spectrum matches that of the global sections of their structure sheaf, providing a positive answer to a question by Kovacic, especially for Ritt algebras.

Contribution

It establishes the equality of differential spectra for Keigher rings and their global sections, resolving a previously open question.

Findings

Differential spectrum of Keigher rings equals that of their global sections

The result applies specifically to Ritt algebras containing rationals

Provides a definitive answer to Kovacic's question

Abstract

Answering a question of J.~Kovacic, we show that, for any Keigher ring, its differential spectrum coincides with the differential spectrum of the ring of global sections of the structure sheaf. In particular, we obtain the answer for Ritt algebras, that is, differential rings containing the rational numbers.