多重性与不可实现的等变链复形
Multiplicativity and nonrealizable equivariant chain complexes
摘要：
设$G$是一个有限的$p$ -群，$\mathbb{F}$是一个具有特征$p$的域.我们用$\mathbb{F} G$的增广理想的幂滤出系数在$\mathbb{F}$中的自由$G$ -空间的上链复形.我们表明，上积引起的乘法结构上出现的谱序列和计算的$E_1$ -页作为一个双阶代数。作为应用，我们证明了最近Iyengar和Walker对Carlsson猜想的一个代数版本的反例不能拓扑实现。
英文摘要：
Let $G$ be a finite $p$-group and $\mathbb{F}$ a field of characteristic $p$. We filter the cochain complex of a free $G$-space with coefficients in $\mathbb{F}$ by powers of the augmentation ideal of $\mathbb{F} G$. We show that the cup product induces a multiplicative structure on the arising spectral sequence and compute the $E_1$-page as a bigraded algebra. As an application, we prove that recent counterexamples of Iyengar and Walker to an algebraic version of Carlsson's conjecture can not be realized topologically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
