2022/04/03 by Charalampos Verasdanis, Verasdanis, Charalampos
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2204.01082
openalex publication_date 2022/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 T0 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 T0 with respect to the small topology.