Back to Search
Start Over
A Zariski--Nagata theorem for smooth ℤ-algebras.
- Source :
-
Journal für die Reine und Angewandte Mathematik . Apr2020, Vol. 2020 Issue 761, p123-140. 18p. - Publication Year :
- 2020
-
Abstract
- In a polynomial ring over a perfect field, the symbolic powers of a prime ideal can be described via differential operators: a classical result by Zariski and Nagata says that the n-th symbolic power of a given prime ideal consists of the elements that vanish up to order n on the corresponding variety. However, this description fails in mixed characteristic. In this paper, we use p-derivations, a notion due to Buium and Joyal, to define a new kind of differential powers in mixed characteristic, and prove that this new object does coincide with the symbolic powers of prime ideals. This seems to be the first application of p-derivations to commutative algebra. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMMUTATIVE algebra
*POLYNOMIAL rings
*PRIME ideals
*DIFFERENTIAL operators
Subjects
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2020
- Issue :
- 761
- Database :
- Academic Search Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 142513734
- Full Text :
- https://doi.org/10.1515/crelle-2018-0012