On Bass' question for finitely generated algebras over large fields

TL;DR

This paper provides a concise alternative proof that finitely generated algebras over large fields of characteristic zero satisfy Bass' question regarding NK-groups, using classical K-theory techniques.

Contribution

It offers a new, shorter proof for Bass' question for finite type algebras over large fields, extending previous results with classical K-theory methods.

Findings

Affirmative answer to Bass' question for finite type algebras over large fields of characteristic zero

Introduction of a K_i-analogue of Murthy-Pedrini's observation from 1972

Simplification of existing proofs using classical higher K-theory techniques

Abstract

Recently Cortinas-Haesemayer-Walker-Weibel gave affirmative answer to Bass' 1972 question on NK-groups for algebras of essentially finite type over large fields of characteristic 0. Here we give an alternative short proof of this result for algebras of finite type over such fields. Our approach is based on classical techniques in higher K-theory of rings and a direct K_i-analogue of an old observation of Murthy-Pedrini, dating back from the same 1972.