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Mathematics > Algebraic Geometry

arXiv:1812.09979 (math)
[Submitted on 24 Dec 2018 (v1), last revised 3 Mar 2020 (this version, v2)]

Title:Cobordism-framed correspondences and the Milnor K-theory

Authors:Aleksei Tsybyshev (St. Petersburg Branch of Steklov Mathematical Institute)
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Abstract:In this work, we compute the $0$th cohomology group of a complex of groups of cobordism-framed correspondences, and prove the isomorphism to Milnor $K$-groups. An analogous result for common framed correspondences has been proved by A. Neshitov in his paper "Framed correspondences and the Milnor---Witt $K$-theory".
Neshitov's result is, at the same time, a computation of the homotopy groups $\pi_{i,i}(S^0)(Spec(k)).$ This work could be used in the future as basis for computing homotopy groups $\pi_{i,i}(MGL_{\bullet})(Spec(k))$ of the spectrum $MGL_{\bullet}.$
Comments: 18 pages
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14F42, 19D45
Cite as: arXiv:1812.09979 [math.AG]
  (or arXiv:1812.09979v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.09979

Submission history

From: Aleksei Tsybyshev MMath [view email]
[v1] Mon, 24 Dec 2018 21:03:41 UTC (12 KB)
[v2] Tue, 3 Mar 2020 11:55:22 UTC (15 KB)
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