DISCLAIMER: This is just a draft. I am not sure of the final purpose of this document, so at the moment I have included lots of known results, in particular proofs of the usual Fundamental Theorem of Galois theory (in the finite and then the algebraic case). Seeing such proofs helps (me) to understand the analogies between the Fundamental Theorem presented here and the usual cases. Also, CAVEAT...

In this paper we show how the restriction of the complex algebraic cycles to real part of a complex algebraic set îs related to the real algebraic cycles of the real part As a corollary we give examples of smooth submanifolds of a Euchdean space which can not be isotoped to real parts of complex nonsingular subvaneties in the corresponding projective space Algebraic numbers are dense in R. The ...