Hermitian lattices and bounds in K-theory of algebraic integers

TL;DR

This paper improves upper bounds on the torsion part of algebraic K-theory for rings of integers in number fields by refining geometric estimates of hermitian lattices, building on Soulé's method.

Contribution

It introduces enhanced estimates for hermitian lattices that lead to tighter bounds in the K-theory of algebraic integers, advancing previous methods.

Findings

Improved upper bounds for torsion in K-theory of algebraic integers

Refined geometric estimates for hermitian lattices

Enhanced methods based on Soulé's approach

Abstract

Elaborating on a method of Soul\'e, and using better estimates for the geometry of hermitian lattices, we improve the upper bounds for the torsion part of the K-theory of the rings of integers of number fields.