The Category-Theoretic Arithmetic of Information

Fuzzy sets form A meta-system-theoretic point of view

Arithmetic Teichmuller Theory

By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing th...

A Finite Order Arithmetic Foundation for Cohomology

Large-structure tools like toposes and derived categories in cohomology never go far from arithmetic in practice, yet existing formalizations are stronger than ZFC. We formalize the practical insight by grounding the entire toolkit of EGA and SGA at the level of finite order arithmetic. Grothendieck pre-empted many set theoretic issues in cohomology by positing a universe: “a set ‘large enough’...

Arithmetic Deformation Theory of Lie Algebras

This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...

Combination of real options and game-theoretic approach in investment analysis

Investments in technology create a large amount of capital investments by major companies. Assessing such investment projects is identified as critical to the efficient assignment of resources. Viewing investment projects as real options, this paper expands a method for assessing technology investment decisions in the linkage existence of uncertainty and competition. It combines the game-theore...