تقرير
The slice spectral sequence for a motivic analogue of the connective $K(1)$-local sphere
| العنوان: | The slice spectral sequence for a motivic analogue of the connective $K(1)$-local sphere |
|---|---|
| المؤلفون: | Kong, Hana Jia, Quigley, J. D. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Topology, 14F42, 55P42, 55Q45, 55Q51 |
| الوصف: | We compute the slice spectral sequence for the motivic stable homotopy groups of $L$, a motivic analogue of the connective $K(1)$-local sphere over prime fields of characteristic not two. Together with the analogous computation over algebraically closed fields, this yields information about the motivic $K(1)$-local sphere over arbitrary base fields of characteristic not two. To compute the slice spectral sequence, we prove several results which may be of independent interest. We describe the $d_1$-differentials in the slice spectral sequence in terms of the motivic Steenrod operations over general base fields, building on analogous results of Ananyevskiy, R{\"o}ndigs, and {\O}stv{\ae}r for the very effective cover of Hermitian K-theory. We also explicitly describe the coefficients of certain motivic Eilenberg--MacLane spectra and compute the slice spectral sequence for the very effective cover of Hermitian K-theory over prime fields. Comment: 36 pages, 16 figures. Comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2209.08603 |
| رقم الأكسشن: | edsarx.2209.08603 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |