论文标题
Equivariant $ \ useverline {\ Mathbb {z}/\ ell} $ - 环状组的模块$ C_2 $
Equivariant $\underline{\mathbb{Z}/\ell}$-modules for the cyclic group $C_2$
论文作者
论文摘要
对于循环组$ c_2 $，我们对常数mackey环$ \ useverline {\ mathbb {z}/\ ell} $的完美模块的派生类别进行完整描述，对于$ \ ell $ a prime。对于$ \ ell $奇数来说，这很简单，但是对于$ \ ell = 2 $，这取决于新的分裂定理。作为拆分定理的推论，我们计算了相关的PICARD组和Balmer Spectrum，用于派生类别中的紧凑型物体，并在$ C_2 $ -CO_2 $ -EQUIVARIANT EILENBERG--MACLANE SPEMERRUM $ H \下列有限模块上获得了有限模块的完整分类。我们还使用拆分定理给出了有关$ RO（C_2）$的一些事实的新的启发性证据，即渐变的Bredon共同体，即Kronholm的FreeNess定理和C. May的结构定理。
For the cyclic group $C_2$ we give a complete description of the derived category of perfect complexes of modules over the constant Mackey ring $\underline{\mathbb{Z}/\ell}$, for $\ell$ a prime. This is fairly simple for $\ell$ odd, but for $\ell=2$ depends on a new splitting theorem. As corollaries of the splitting theorem we compute the associated Picard group and the Balmer spectrum for compact objects in the derived category, and we obtain a complete classification of finite modules over the $C_2$-equivariant Eilenberg--MacLane spectrum $H\underline{\mathbb{Z}/2}$. We also use the splitting theorem to give new and illuminating proofs of some facts about $RO(C_2)$-graded Bredon cohomology, namely Kronholm's freeness theorem and the structure theorem of C. May.
