论文标题
动机和真正的王权的跨色素扩展
Transchromatic extensions in motivic and Real bordism
论文作者
论文摘要
我们在动机Bordism Spectrum $ MGL $和真正的Bordism Spectrum Spectrum $ MU _ {\ Mathbb r} $的同型中显示了许多Toda括号。从某种意义上说，尽管括号中的术语为某种色度$ n $，但这些括号是“红色转移”，但支架本身将为色度高$（n+1）$。使用这些，我们在$π_ {（\ ast，\ ast）} mgl $ -Module结构中推断出一个异国情调的乘法家族，即动机Morava $ k $ - 包括非客气乘法，包括$ 2 $。这些反过来暗示了$π_ {\ star} mu_ \ mathbb r $-模块结构的类似乘数的类似家族。
We show a number of Toda brackets in the homotopy of the motivic bordism spectrum $MGL$ and of the Real bordism spectrum $MU_{\mathbb R}$. These brackets are "red-shifting" in the sense that while the terms in the bracket will be of some chromatic height $n$, the bracket itself will be of chromatic height $(n+1)$. Using these, we deduce a family of exotic multiplications in the $π_{(\ast,\ast)}MGL$-module structure of the motivic Morava $K$-theories, including non-trivial multiplications by $2$. These in turn imply the analogous family of exotic multiplications in the $π_{\star}MU_\mathbb R$-module structure on the Real Morava $K$-theories.
