分层与粉碎谱
Stratification and the smashing spectrum
AI总结：
本文为刚性紧生成张量三角范畴发展分层理论，利用粉碎谱和小粉碎支撑，证明望远镜猜想与同调谱的$T_0$性及同调支撑检测消失性等价，并建立下降定理。
摘要：
我们利用粉碎谱和小粉碎支撑，为刚性紧生成张量三角范畴发展了分层理论。在分层背景下，我们研究了大概理想、对象态素理想与同调素理想之间的联系，并证明了望远镜猜想成立当且仅当同调谱是$T_0$的且同调支撑能检测消失性。我们还将分层归结为粉碎局部化。此外，我们研究了粉碎谱之间的诱导映射，并证明了分层的下降定理。在分层背景之外，我们证明了望远镜猜想成立当且仅当粉碎谱在小拓扑下是$T_0$的。
英文摘要：
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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