Real Algebraic and Analytic Geometry |

Weighted sums of squares in local rings and their completions, I.

e-mail:

homepage: http://www.math.uni-konstanz.de/~scheider/index.html

Submission: 2009, February 20.

*Abstract:
Let A be an excellent local ring of real dimension at most 2, let
T be a finitely generated preordering in A, and let T' be the
preordering generated by T in the completion A' of A. Under a
weak condition on the residue field k = A/m we show that T
saturated implies T' saturated, and that a weak version of the
converse holds as well. We also prove a transfer result between
different real closed fields in the case where A is henselian and
k is real closed. These results have direct implications for
nonnegativity certificates for real polynomials which are nonnegative
on suitable 2-dimensional semi-algebraic sets.*

Mathematics Subject Classification (2000): 14P99,13H05,14P10,32S05.

Keywords and Phrases: Local rings, completion, Artin approximation, preorderings, curve singularities, positive polynomials, sums of squares, real algebraic geometry.

**Full text**, 20p.:
dvi 173k,
pdf 307k.

Server Home Page