论文标题
分层和粉碎光谱
Stratification and the smashing spectrum
论文作者
论文摘要
我们开发了使用粉碎光谱和小型粉碎支持的刚性结构产生的张张量三角构调节类别的分层理论。在分层的环境中，我们研究了大素数理想，objectwise-prime理想和同源素数之间的联系，并且我们表明望远镜的猜想才能达到，并且仅当同源频谱为$ t_0 $时，并且同源支持检测到消失。我们还将分层减少到粉碎本地化。此外，我们研究了粉碎光谱之间的诱导图，并证明了分层的下降定理。在分层的上下文之外，我们证明望远镜的猜想在且仅当相对于小拓扑相对于粉碎频谱为$ T_0 $时。
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.
