On the algebraic K-theory of Spec Z^N

TL;DR

This paper explores the algebraic K-theory of a projective system of generalized schemes arising from Arakelov geometry, providing new algebraic insights into the spectrum of integers.

Contribution

It introduces a novel algebraic framework for Arakelov compactification and computes the algebraic K-theory of its constituents, advancing the understanding of algebraic geometry over Spec Z^N.

Findings

Computed algebraic K-theory of constituents in the projective system

Constructed Arakelov compactification algebraically

Analyzed the structure of generalized schemes

Abstract

In his thesis, N. Durov develops a theory of algebraic geometry in which schemes are locally determined by commutative algebraic monads. In this setting, one is able to construct the Arakelov geometric compactification of the spectrum of the ring of integers in a purely algebraic fashion. This object arises as the limit of a certain projective system of generalized schemes. We study the constituents of this projective system, and compute their algebraic K-theory.