论文标题
奇异的$ k（2）$ - prime $ 2 $的本地Picard Group
The Exotic $K(2)$-Local Picard Group at the Prime $2$
论文作者
论文摘要
我们计算了$ k（2）$ - prime $ 2 $的本地Picard Group中的$κ_2$的组$κ__2$，发现它是一组订单$ 2^9 $ iSomorphic to $（\ Mathbb {z}/8）^2 \ times（\ Mathbb {Z}/2）^3 $。为了做到这一点，我们必须定义和利用Picard组中构造元素的各种不同方式，这需要对理论进行重大探索。到目前为止，最具创新性的技术在Prime $ 2 $上运作效果最佳，是使用$ J $ - 肌形态，从Morava Stapilizer Group的有限商的真实表示形成组到$ K（n）$ - 本地Picard Group。
We calculate the group $κ_2$ of exotic elements in the $K(2)$-local Picard group at the prime $2$ and find it is a group of order $2^9$ isomorphic to $(\mathbb{Z}/8)^2 \times (\mathbb{Z}/2)^3$. In order to do this we must define and exploit a variety of different ways of constructing elements in the Picard group, and this requires a significant exploration of the theory. The most innovative technique, which so far has worked best at the prime $2$, is the use of a $J$-homomorphism from the group of real representations of finite quotients of the Morava stabilizer group to the $K(n)$-local Picard group.
