Sur le spectre réel des anneaux locaux complets.

Abstract

We study the real spectrum of complete local rings with real closed residue field. We show that for every constructible subset C the following hold: (1) the closure C of C is constructible, and (2) C has a finite number of connected components and these are constructible. Also we define semialgebroid sets and show that they satisfy the same ‘elementary’ properties as semialgebraic sets.