On split Steinberg modules and Steinberg modules

TL;DR

This paper proves that the natural maps from split Steinberg modules to Steinberg modules over Dedekind domains are surjective, answering a question posed by Randal-Williams.

Contribution

It establishes the surjectivity of natural maps between split Steinberg modules and Steinberg modules over Dedekind domains, addressing an open question.

Findings

Surjective maps from split Steinberg modules to Steinberg modules over Dedekind domains.

Resolution of Randal-Williams' question on module maps.

Advancement in understanding Steinberg modules in algebraic K-theory.

Abstract

Answering a question of Randal-Williams, we show the natural maps from split Steinberg modules of a Dedekind domain to the associated Steinberg modules are surjective.