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Mathematics > Algebraic Geometry

arXiv:1809.00087 (math)
[Submitted on 31 Aug 2018 (v1), last revised 13 Dec 2018 (this version, v6)]

Title:The homomorphism of presheaves ${\mathrm{K}}^\mathrm{MW}_*\to π^{*,*}_s$ over a base

Authors:A. Druzhinin
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Abstract:We construct the homomorphism of presheaves ${\mathrm{K}}^\mathrm{MW}_* \to {\pi}^{*,*}$ over an arbitrary base scheme $S$, where $\mathrm{K}^\mathrm{MW}$ is the (naive) Milnor-Witt K-theory presheave.
Also we discuss some partly alternative proof (or proofs) of the isomorphism of sheaves $\unKMW_n\simeq \underline{\pi}^{n,n}_s$, $n\in \mathbb Z$, over a filed $k$ originally proved in \cite{M02} and \cite{M-A1Top}.
Comments: We add a proof of the isomorphism over a field
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14F42, 19E20
Cite as: arXiv:1809.00087 [math.AG]
  (or arXiv:1809.00087v6 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1809.00087
Journal reference: Ann. K-Th. 6 (2021) 651-671
Related DOI: https://doi.org/10.2140/akt.2021.6.651

Submission history

From: Andrei Druzhinin [view email]
[v1] Fri, 31 Aug 2018 23:53:07 UTC (10 KB)
[v2] Tue, 11 Sep 2018 06:32:33 UTC (10 KB)
[v3] Mon, 8 Oct 2018 13:22:06 UTC (15 KB)
[v4] Sun, 14 Oct 2018 15:56:29 UTC (16 KB)
[v5] Wed, 12 Dec 2018 18:56:03 UTC (34 KB)
[v6] Thu, 13 Dec 2018 14:53:59 UTC (32 KB)
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