Homology of $\GL_n$ over infinite fields outside the stability range
Abstract
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 $n\leq 4$.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2020
- DOI:
- 10.48550/arXiv.2011.03820
- arXiv:
- arXiv:2011.03820
- Bibcode:
- 2020arXiv201103820M
- Keywords:
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- Mathematics - K-Theory and Homology;
- Primary: 19D55;
- 19D45;
- Secondary: 20J06
- E-Print:
- 26 pages, Latex