论文标题
根，代数$ k $ - 理论和色度红移的邻接
Adjunction of roots, algebraic $K$-theory and chromatic redshift
论文作者
论文摘要
给定一个满足合适假设的$ e_1 $ -ring $ a $和a类$ a \ inπ_{mk}（a）$，我们定义了$ e_1 $ -rings $ a \ a \ a（\ sqrt [m] {a}）的地图，以实现$ m $ th $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a的邻接我们为$ e_1 $ rings定义了一种对数的形式，并表明root auckunction是适当驯服的扩展名的log-thh-étale，它为thh $（\ sqrt [m] {a} a}）提供了一个公式，以thh和thh的thh和log-thh thh和$ a $ a $ a $ a $ a $。如果$ a $是结缔组织，我们证明诱导的映射$ k（a）\ to k（a（\ sqrt [m] {a}））$ in engebraic $ k $ - 理论是包括楔形总结。使用此情况，我们获得$ v（1）_*k（ko_p）$ for $ p> 3 $，而且，我们推断出，如果$ k（a）$展示了色度红移，那么$ k（a（\ sqrt [m] {a}}））$。我们将环光谱的几种扩展解释为根接节的示例，并使用它来获得新的证明，证明了卢宾 - 泰特光谱满足红移猜想的事实。
Given an $E_1$-ring $A$ and a class $a \in π_{mk}(A)$ satisfying a suitable hypothesis, we define a map of $E_1$-rings $A\to A(\sqrt[m]{a})$ realizing the adjunction of an $m$th root of $a$. We define a form of logarithmic THH for $E_1$-rings, and show that root adjunction is log-THH-étale for suitably tamely ramified extension, which provides a formula for THH$(A(\sqrt[m]{a}))$ in terms of THH and log-THH of $A$. If $A$ is connective, we prove that the induced map $K(A) \to K(A(\sqrt[m]{a}))$ in algebraic $K$-theory is the inclusion of a wedge summand. Using this, we obtain $V(1)_*K(ko_p)$ for $p>3$ and also, we deduce that if $K(A)$ exhibits chromatic redshift, so does $K(A(\sqrt[m]{a}))$. We interpret several extensions of ring spectra as examples of root adjunction, and use this to obtain a new proof of the fact that Lubin-Tate spectra satisfy the redshift conjecture.
