|
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2004, Volume 246, Pages 106–115
(Mi tm148)
|
|
|
|
This article is cited in 24 scientific papers (total in 25 papers)
On the Zero Slice of the Sphere Spectrum
V. A. Voevodskii Institute for Advanced Study, School of Mathematics
Abstract:
We prove the motivic analogue of the statement saying that the zero stable homotopy group of spheres is $\mathbf Z$. In topology, this is equivalent to the fact that the fiber of the obvious map from the sphere $S^n$ to the Eilenberg–MacLane space $K(\mathbf Z,n)$ is $(n+1)$-connected. We prove our motivic analogue by an explicit geometric investigation of a similar map in the motivic world. Since we use the model of the motivic Eilenberg–MacLane spaces based on the symmetric powers, our proof works only in zero characteristic.
Received in February 2004
Citation:
V. A. Voevodskii, “On the Zero Slice of the Sphere Spectrum”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 246, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 106–115; Proc. Steklov Inst. Math., 246 (2004), 93–102
Linking options:
https://www.mathnet.ru/eng/tm148 https://www.mathnet.ru/eng/tm/v246/p106
|
|