Druzhinin, Andrei The naive Milnor-Witt \(K\)-theory relations in the stable motivic homotopy groups over a base. (English) Zbl 1483.14041 Ann. \(K\)-Theory 6, No. 4, 651-671 (2021). Summary: We extend the canonical homomorphism between the (naive) Milnor-Witt \(K\)-theory presheaf and the presheaf of stable motivic homotopy groups \[ \mathrm{K}^{\mathrm{MW}}_n(\text{--})\to\pi^{n,n}_s(\text{--}),\quad n\in\mathbb Z, \] from the base field case to the case of any base scheme \(S\). MSC: 14F42 Motivic cohomology; motivic homotopy theory 19E08 \(K\)-theory of schemes 19E20 Relations of \(K\)-theory with cohomology theories Keywords:Milnor-Witt \(K\)-theory; stable motivic homotopy groups; motivic homotopy category over a base PDFBibTeX XMLCite \textit{A. Druzhinin}, Ann. \(K\)-Theory 6, No. 4, 651--671 (2021; Zbl 1483.14041) Full Text: DOI References: [1] 10.1016/S0764-4442(99)80120-7 · Zbl 0944.20027 · doi:10.1016/S0764-4442(99)80120-7 [2] 10.1016/j.aim.2015.09.014 · Zbl 1335.11030 · doi:10.1016/j.aim.2015.09.014 [3] 10.2140/agt.2014.14.3603 · Zbl 1351.14013 · doi:10.2140/agt.2014.14.3603 [4] 10.1155/S1073792801000447 · Zbl 0994.19002 · doi:10.1155/S1073792801000447 [5] ; Hutchinson, Doc. Math., 267 (2010) [6] ; Jardine, Doc. Math., 5, 445 (2000) · Zbl 0969.19004 [7] ; Mazza, Lecture notes on motivic cohomology. Clay Mathematics Monographs, 2 (2006) · Zbl 1115.14010 [8] 10.1016/S0764-4442(99)80306-1 · Zbl 0937.19002 · doi:10.1016/S0764-4442(99)80306-1 [9] ; Morel, Contemporary developments in algebraic K-theory. ICTP Lect. Notes, XV, 357 (2004) [10] 10.1007/978-94-007-0948-5_7 · doi:10.1007/978-94-007-0948-5_7 [11] 10.1007/s00014-004-0815-z · Zbl 1061.19001 · doi:10.1007/s00014-004-0815-z [12] 10.1007/978-3-642-29514-0 · Zbl 1263.14003 · doi:10.1007/978-3-642-29514-0 [13] ; Morel, Inst. Hautes Études Sci. Publ. Math., 90, 45 (1999) · Zbl 0983.14007 [14] 10.1017/S1474748016000190 · Zbl 1407.14016 · doi:10.1017/S1474748016000190 [15] 10.1070/IM1990v034n01ABEH000610 · Zbl 0684.18001 · doi:10.1070/IM1990v034n01ABEH000610 [16] 10.4007/annals.2007.165.1 · Zbl 1124.14017 · doi:10.4007/annals.2007.165.1 [17] 10.1016/j.aim.2017.08.034 · Zbl 1387.19002 · doi:10.1016/j.aim.2017.08.034 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.