论文标题
当地的Gorenstein二元性二元性
Local Gorenstein duality for cochains on spaces
论文作者
论文摘要
我们调查何时何时可交换环频谱$ r $满足当地戈伦斯坦二元性的同型版本，从而扩展了格林利斯先前研究的概念。为了做到这一点，我们证明了沿$ k $ - 代数的形态沿当地戈伦斯坦二元性的上升定理。我们的主要示例是$ r = c^*（x; k）$的形式，是field $ k $的空格$ x $上的cochains的环谱。特别是，我们在特征$ p $中建立了本地的戈伦斯坦二重性，用于$ p $ - compact群体和$ p $ - 局部有限群，以及$ k = \ q $和$ x $ a简单地连接的空间，这是戈伦斯坦（Gorenstein），这是Dwyer，Greenlees和Iyengar的感觉。
We investigate when a commutative ring spectrum $R$ satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to do this, we prove an ascent theorem for local Gorenstein duality along morphisms of $k$-algebras. Our main examples are of the form $R = C^*(X;k)$, the ring spectrum of cochains on a space $X$ for a field $k$. In particular, we establish local Gorenstein duality in characteristic $p$ for $p$-compact groups and $p$-local finite groups as well as for $k = \Q$ and $X$ a simply connected space which is Gorenstein in the sense of Dwyer, Greenlees, and Iyengar.
