Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings
| Autor: | Fernando, José F. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales. Serie A. Matem\'aticas RACSAM 116 (2022), no. 1, Paper 59 (65 pages) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s13398-021-01202-4 |
| Popis: | A classical problem in real geometry concerns the representation of positive semidefinite elements of a ring $A$ as sums of squares of elements of $A$. If $A$ is an excellent ring of dimension $\geq3$, it is already known that it contains positive semidefinite elements that cannot be represented as sums of squares in $A$. The one dimensional local case has been afforded by Scheiderer (mainly when its residue field is real closed). In this work we focus on the $2$-dimensional case and determine (under some mild conditions) which local excellent henselian rings $A$ of embedding dimension $3$ have the property that every positive semidefinite element of $A$ is a sum of squares of elements of $A$. Comment: 55 pages |
| Databáze: | arXiv |
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