Inside our approach to the Model Spec

In this paper, we introduce a new algebraic type of `convexoid rings', and we give the definition of (weak) convexoid schemes, which share similar properties with ordinary schemes. As a result, we give a purely-algebraic construction of the compactification of Spec Z (in Arakelov's sense) which is realized as the Zariski-Riemann space in the category of weak convexoid schemes.

We recover some data of a module $M$ from the Ext-family $\{\Ext^i_R(M,R)\}$. In this regard, we investigate homological subsets of $\Spec(R)$, defined by the help of Ext-family. We extend Grothendieck's calculation of $\dim(\Ext^g_R(M,R))$. Also, we compute support and the set of all associated prime ideals of the Ext-family in a serial of nontrivial cases.

The structure of the standard model is concisely summarized, including the standard model Lagrangian, spontaneous symmetry breaking, the reexpression of the Lagrangian in terms of mass eigenstates after symmetry breaking, and the gauge interactions. The problems of the standard model are described.