Year: 2026
Type: preprint
Abstract: In [B2] Balmer introduced the homological spectrum of a rigid tensor-triangulated category, and had the ``nerves of steel'' not to conjecture that it was in bijection with the prime spectrum, despite an ``avalanche of examples''. Naturally, the statement came to be known as Balmer's Nerves of Steel Conjecture. More recently, in [NVY] the conjecture was stated explicitly and extended to a more general non-symmetric context. In this paper we provide a counterexample to the original suggestion in [B2], so also to the conjecture from [NVY]. A first counterexample was recently constructed in [BHR].
Source: arXiv (Cornell University)
Author: Coulembier, Kevin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Australian Research Council
OpenAlex ID: W7208747814