13 papers · 1 filter
Sites and Grothendieck Topologies, Sites and Sheaves
Arvid Siqveland
We give the minimum of category theory necessary for understanding the definition and applications of Grothendieck topos. We state the basic properties of sites and sheaves, and gi…
Connections on Associative Varieties
Arvid Siqveland
We have embedded the category of smooth real -manifolds faithfully into the category of associative varieties, \cite{S2603}. Many constructions on smooth manifolds can then be g…
Riemannian Geometry on Associative Varieties
Arvid Siqveland
We prove that the classical algebraic varieties over algebraically closed fields can be defined over arbitrary fields Then we prove that for associative algebras , there ex…
Associative Schemes and Subschemes
Arvid Siqveland
In the preprint arXiv:2511.07900 we proved that there exists a localizing ring for an associative ring with unit, and a direct sum of simp…
Localization in Associative Rings
Arvid Siqveland
In arXiv:2511.04191 we constructed schemes of objects in small categories which contained a set of basepoints with local representing (localizing) objects. Here we prove that the c…
Schemes of Objects in Abelian Categories
Arvid Siqveland
In the article Categorical Construction of Schemes, arXiv:2511.03433 we gave a natural definition of ordinary schemes based on the fact that the localization of a ring in a maximal…