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arXiv · 2407.11791

Classifying smashing ideals in derived categories of valuation domains

Scott Balchin·Florian Tecklenburg
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Abstract

Building on results of Bazzoni-\v{S}\v{t}ov\'{\i}\v{c}ek, we give a complete classification of the frame of smashing ideals for the derived category of a finite dimensional valuation domain. In particular, we give an explicit construction of an infinite family of commutative rings such that the telescope conjecture fails and which generalise an example of Keller. As a consequence, we deduce that the Krull dimension of the Balmer spectrum and the Krull dimension of the smashing spectrum can differ arbitrarily for rigidly-compactly generated tensor-triangulated categories.

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Scott Balchin, Florian Tecklenburg. 2024-07-16. Classifying smashing ideals in derived categories of valuation domains. https://arxiv.org/abs/2407.11791

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