论文标题
下降和消失的色度代数$ k $ - 理论通过小组动作
Descent and vanishing in chromatic algebraic $K$-theory via group actions
论文作者
论文摘要
我们证明了一些$ k $ - 理论下降结果，用于稳定的$ \ infty $ - 类别的有限小组动作，包括澳大利亚人的$ p $ - 群体案例的$ p $ - 组案例。我们还根据Ausoni-Rognes的红移哲学证明了消失的结果：尤其是，我们表明，如果$ r $是$ \ Mathbb {e} _ \ infty $ -ring spectrum，则具有$ l_ {t（t（n）} r = 0 $，则$ l_ {t（n），然后$ l_ {t（n+1）} k（n+1）} k（r）= 0 $。我们的主要观察结果是，下降和消失在逻辑上相互关联，允许通过归纳在高度上同时建立它们。
We prove some $K$-theoretic descent results for finite group actions on stable $\infty$-categories, including the $p$-group case of the Galois descent conjecture of Ausoni-Rognes. We also prove vanishing results in accordance with Ausoni-Rognes's redshift philosophy: in particular, we show that if $R$ is an $\mathbb{E}_\infty$-ring spectrum with $L_{T(n)}R=0$, then $L_{T(n+1)}K(R)=0$. Our key observation is that descent and vanishing are logically interrelated, permitting to establish them simultaneously by induction on the height.
