Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings

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Fernando Galván, José Francisco (2022) Representation of positive semidefinite elements as sum of squares in 2-dimensional local rings. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 116 (2). ISSN 1578-7303

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Official URL: https://doi.org/10.1007/s13398-021-01202-4



Abstract

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 ≥3, 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.


Item Type:Article
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CRUE-CSIC (Acuerdos Transformativos 2022)

Uncontrolled Keywords:Real spectrum; Positive semidefinite elements; Sums of squares; Singularities; Excellent henselian ring; Dimension 2; Completion
Subjects:Sciences > Mathematics > Algebraic geometry
Sciences > Mathematics > Group Theory
ID Code:72538
Deposited On:27 May 2022 14:59
Last Modified:30 May 2022 07:06

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