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arXiv · 2204.01082

Stratification and the smashing spectrum

Charalampos Verasdanis
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Abstract

We develop the theory of stratification for a rigidly-compactly generated tensor-triangulated category using the smashing spectrum and the small smashing support. Within the stratified context, we investigate connections between big prime ideals, objectwise-prime ideals and homological primes, and we show that the Telescope Conjecture holds if and only if the homological spectrum is $T_0$ and the homological support detects vanishing. We also reduce stratification to smashing localizations. Moreover, we study induced maps between smashing spectra and prove a descent theorem for stratification. Outside the stratified context, we prove that the Telescope Conjecture holds if and only if the smashing spectrum is $T_0$ with respect to the small topology.

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Charalampos Verasdanis. 2022-04-03. Stratification and the smashing spectrum. https://arxiv.org/abs/2204.01082

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