A Differential Analog of the Noether Normalization Lemma. (24th December 2016)

• Record Type: Journal Article
• Authors: Pogudin, Gleb
• Is Part Of: International mathematics research notices. Volume 2018:Number 4(2018)
• Page Start: 1177
• Page End: 1199
• Publication Date: 2016-12-24
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnw275
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: In this paper, we prove the following differential analog of the Noether normalization lemma: for every $d$ -dimensional differential algebraic variety over differentially closed field of zero characteristic there exists a surjective map on to the $d$ -dimensional affine space. Equivalently, for every integral differential algebra $A$ over differential field of zero characteristic there exist differentially independent $b_1, \ldots, b_d$ such that $A$ is differentially algebraic over subalgebra $B$ differentially generated by $b_1, \ldots, b_d$, and whenever $\mathfrak{p} \subset B$ is a prime differential ideal, there exists a prime differential ideal $\mathfrak{q} \subset A$ such that $\mathfrak{p} = B \cap \mathfrak{q}$ . We also prove the analogous theorem for differential algebraic varieties over the ring of formal power series over an algebraically closed differential field and present some applications to differential equations.