Some properties of G-schemes

Abstract

In this paper, we continue to adapt the theories of spectra and schemes developed by Grothendieck in algebraic geometry to the category of groups. Let $G$ be a group, and $(H,f_G^H)$ and object of the comma category $C(G)$. In [5], we have defined on the set $Spec_G(H)$ of prime ideals of $(H,f_G^H)$ a topology. In this paper, we define another notion of prime ideals to which we associate a spectrum endowed with a topology. We study some properties and objects associated to these spectra; amongst them we can quote, irreducibility, the radical, the structural sheaf, $G$-varieties and $G$-schemes. \bigskip