TL;DR
This paper develops a generalized theory of prolongation spaces for algebraic varieties, connecting them with jet spaces through an interpolating map, applicable across difference and differential contexts.
Contribution
It introduces a unified framework for prolongation spaces that encompasses difference and differential algebraic geometry, along with an interpolating map to jet spaces.
Findings
Prolongation spaces are generalized in an abstract setting.
An interpolating map between prolongation and jet spaces is constructed.
The framework applies to difference and differential algebraic varieties.
Abstract
The notion of prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares the prolongation spaces with algebraic jet spaces is introduced and studied.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Topics in Algebra