Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 207-02. The Bass trace conjecture and the characteristic-zero Kaplansky idempotent conjecture
Manuscript map · lines 6095–6104
OpenAI@2026-10-07#rem:oai-p-207-02
Authors: OpenAI. Family 207.
Title: The Bass trace conjecture and the characteristic-zero Kaplansky idempotent conjecture.
Abstract: We prove the complex group-ring Bass trace conjecture for every discrete group: the Hattori–Stallings trace of a finitely generated projective module over its complex group ring is supported on conjugacy classes of finite-order elements. As a consequence, for every torsion-free group G and every commutative unital domain R of characteristic zero, the only idempotents in $RG$ are 0 and 1. This proves Kaplansky's idempotent conjecture in characteristic zero.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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