对“钢铁神经猜想”的又一反例

中文摘要 AI 辅助

在[B2]中，Balmer引入了刚性张量三角范畴的同伦谱，尽管存在“大量例子”，他仍大胆提出其与素谱一一对应的猜想，该猜想后来被称为Balmer的“钢铁神经猜想”。最近，[NVY]明确表述了该猜想并将其扩展到更一般的非对称语境。本文为[B2]中的原始断言提供了一个反例，因此也反驳了[NVY]中的猜想。最近[BHR]中已构造出第一个反例。

英文摘要

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].

发表机构

• University of Sydney（悉尼大学）

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