The first smooth intersections of two quadrics in P^5 and cubic threefolds in P^4 over the real Puiseux series field are semi-algebraically connected but not stably rational.
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Vari\'et\'es r\'eelles connexes non stablement rationnelles
The first smooth intersections of two quadrics in P^5 and cubic threefolds in P^4 over the real Puiseux series field are semi-algebraically connected but not stably rational.