The real spectrum of an ideal and KO-theory exact sequences

K-Theory ◽  
1987 ◽  
Vol 1 (3) ◽  
pp. 211-235 ◽  
Author(s):  
G. W. Brumfiel
Keyword(s):  
Real Spectrum ◽  
The Real ◽  
Exact Sequences

The portion of matrices with real spectrum in the real orthogonal Lie algebra

2016 ◽  
Vol 57 (2) ◽  
pp. 303-321
Author(s):  
A. S. Krivonogov ◽  
V. A. Churkin
Keyword(s):  
Lie Algebra ◽  
Real Spectrum ◽  
The Real ◽  
Orthogonal Lie Algebra

scholarly journals Real Tropicalization and Analytification of Semialgebraic Sets

2020 ◽  
Author(s):  
Philipp Jell ◽  
Claus Scheiderer ◽  
Josephine Yu
Keyword(s):  
Inverse Limit ◽  
Point Of View ◽  
General Point ◽  
Real Spectrum ◽  
Closed Field ◽  
Topological Properties ◽  
Absolute Value ◽  
The Real ◽  
Semialgebraic Set ◽  
Refined Version

Abstract Let $K$ be a real closed field with a nontrivial non-archimedean absolute value. We study a refined version of the tropicalization map, which we call real tropicalization map, that takes into account the signs on $K$. We study images of semialgebraic subsets of $K^n$ under this map from a general point of view. For a semialgebraic set $S \subseteq K^n$ we define a space $S_r^{{\operatorname{an}}}$ called the real analytification, which we show to be homeomorphic to the inverse limit of all real tropicalizations of $S$. We prove a real analogue of the tropical fundamental theorem and show that the tropicalization of any semialgebraic set is described by tropicalization of finitely many inequalities, which are valid on the semialgebraic set. We also study the topological properties of real analytification and tropicalization. If $X$ is an algebraic variety, we show that $X_r^{{\operatorname{an}}}$ can be canonically embedded into the real spectrum $X_r$ of $X$, and we study its relation with the Berkovich analytification of $X$.

scholarly journals Nonselfadjoint correct restrictions and extensions with the real spectrum

2014 ◽  
Author(s):  
Bazarkhan Nuraldinovich Biyarov ◽  
Madi Raikhan
Keyword(s):  
Real Spectrum ◽  
The Real

scholarly journals Semi-algebraic decision complexity, the real spectrum, and degree

1996 ◽  
Vol 110 (2) ◽  
pp. 131-184 ◽  
Author(s):  
Thomas Lickteig
Keyword(s):  
Real Spectrum ◽  
The Real ◽  
Decision Complexity

Complete Ideals Defined by Sign Conditions and the Real Spectrum of a Two-dimensional Local Ring

1995 ◽  
Vol 174 (1) ◽  
pp. 21-34 ◽  
Author(s):  
Dean Alvis ◽  
Bernhard L. Johnston ◽  
James J. Madden
Keyword(s):  
Local Ring ◽  
Real Spectrum ◽  
Two Dimensional ◽  
The Real ◽  
Sign Conditions

The portion of matrices with real spectrum in the Lie algebra of the real symplectic group

2014 ◽  
Vol 55 (6) ◽  
pp. 1056-1072 ◽  
Author(s):  
A. S. Krivonogov ◽  
V. A. Churkin
Keyword(s):  
Lie Algebra ◽  
Symplectic Group ◽  
Real Spectrum ◽  
The Real ◽  
Real Symplectic Group
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