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The ℓ¹-Bass conjecture for all discrete groups
Proves the ℓ-Bass conjecture for every discrete group: Hattori–Stallings traces of idempotent matrices over are supported on finitely many finite-order conjugacy classes. The algebraic companion proves the integral Bass trace conjecture and Kaplansky's idempotent conjecture for torsion-free groups over every commutative unital characteristic-zero domain.
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The ℓ¹-Bass Conjecture for Discrete Groups
Oct 5, 2026·l1-bass-conjecture.pdf
We prove the ℓ-Bass conjecture for every discrete group. The Hattori–Stallings trace of every idempotent matrix over the complex ℓ group algebra is supported on finitely many conjugacy classes of finite-order elements.
The Bass trace conjecture and the characteristic-zero Kaplansky idempotent conjecture
Sep 24, 2026·The-Bass-trace-conjecture-for-complex-group-rings-September-24-2026.pdfLean
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 are 0 and 1. This proves Kaplansky's idempotent conjecture in characteristic zero.