Amartya Goswami - K-spaces of non-domain-valued geometric points

The aim of this talk is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a k-algebra and this new “k-space” becomes a generalization of the corresponding Zariski space. We prove that a k-space is T0, quasi-compact, spectral, and connected. Moreover, we study continuous maps between such k-spaces. We conclude with a problem of construct-ing a sheaf of local rings of k-spaces, similar to affine schemes.