论文标题
彩色无效
The Chromatic Nullstellensatz
论文作者
论文摘要
我们表明，在$ t（n）$ - 本地$ \ mathbb {e} _ {\ infty} $中，附加到代数封闭字段的lubin-tate理论是在满足希尔伯特nullstellenstellensatz的模拟的$ t（n）$中。此外，我们表明，对于每$ t（n）$ - 本地$ \ mathbb {e} _ {\ infty} $ - ring $ r $，收集$ \ mathbb {e} _ \ infty $ - iffty $ - r $ $ r $从$ r $从$ r $到这种Lubin-tate TATE TATE TATE TATE TATE TATE TATE tate tate tate tate tate nillply nililpotence。特别是，我们推断出每个非零$ t（n）$ - 本地$ \ mathbb {e} _ {\ infty} $ - ring $ r $允许到$ \ mathbb {e} _ \ infty $ -ring $ - infty $ - rubin-lubin-tate理论。作为结果，我们构造了$ \ mathbb {e} _ {\ infty} $代数封闭的lubin-tate理论的复杂方向，计算此类lubin-tate理论的严格PICARD光谱，并证明了代数$ \ Mathrm {k} $ - 理论的redshift $ \ mathbb {e} _ {\ infty} $ - 戒指。
We show that Lubin--Tate theories attached to algebraically closed fields are characterized among $T(n)$-local $\mathbb{E}_{\infty}$-rings as those that satisfy an analogue of Hilbert's Nullstellensatz. Furthermore, we show that for every $T(n)$-local $\mathbb{E}_{\infty}$-ring $R$, the collection of $\mathbb{E}_\infty$-ring maps from $R$ to such Lubin-Tate theories jointly detect nilpotence. In particular, we deduce that every non-zero $T(n)$-local $\mathbb{E}_{\infty}$-ring $R$ admits an $\mathbb{E}_\infty$-ring map to such a Lubin-Tate theory. As consequences, we construct $\mathbb{E}_{\infty}$ complex orientations of algebraically closed Lubin-Tate theories, compute the strict Picard spectra of such Lubin-Tate theories, and prove redshift for the algebraic $\mathrm{K}$-theory of arbitrary $\mathbb{E}_{\infty}$-rings.
