论文标题
$ \ gl_n $在稳定范围之外的无限字段上的同源性
Homology of $\GL_n$ over infinite fields outside the stability range
论文作者
论文摘要
对于无限字段$ f $，我们研究地图的内核$ h_ {n}（\ mathrm {gl} _ {n-1}（f）（f），\ mathbb {z} \ big [\ frac {1} h_ {n}（\ mathrm {gl} _ {n}（f），\ mathbb {z} \ big [\ frac {\ frac {1} {（m-2）！} \ big]）$ $ h_ {n+1} \ big（\ mathrm {gl} _ {n-1}（f），\ mathbb {z} \ big [\ frac {1} {（m-2）！} \ big] \ big] \ big）\ to h_ {n+1} \ big（\ mathrm {gl} _ {n}（f），\ mathbb {z} \ big [\ frac {1} {（m-2）{（m-2）！} \ big] \ big）$。我们对这些内核和焦点进行了猜想的估计，并证明了我们的猜想为$ n \ leq 4 $。
For an infinite field $F$, we study the kernel of the map $H_{n}(\mathrm{GL}_{n-1}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big]) \to H_{n}(\mathrm{GL}_{n}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big])$ and the cokernel of $H_{n+1}\Big(\mathrm{GL}_{n-1}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big]\Big) \to H_{n+1}\Big(\mathrm{GL}_{n}(F),\mathbb{Z}\Big[\frac{1}{(m-2)!}\Big]\Big)$. We give conjectural estimates of these kernels and cokernels and prove our conjectures for $n\leq 4$.
