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Medientyp: E-Artikel Titel: FRAMED CORRESPONDENCES AND THE MILNOR–WITT -THEORY Beteiligte: Neshitov, Alexander Erschienen: Cambridge University Press (CUP), 2018 Erschienen in: Journal of the Institute of Mathematics of Jussieu, 17 (2018) 4, Seite 823-852 Sprache: Englisch DOI: 10.1017/s1474748016000190 ISSN: 1474-7480; 1475-3030 Schlagwörter: General Mathematics Entstehung: Anmerkungen: Beschreibung: <jats:p>Given a field<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1474748016000190_inline3" /><jats:tex-math>$k$</jats:tex-math></jats:alternatives></jats:inline-formula>of characteristic zero and<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1474748016000190_inline4" /><jats:tex-math>$n\geqslant 0$</jats:tex-math></jats:alternatives></jats:inline-formula>, we prove that<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1474748016000190_inline5" /><jats:tex-math>$H_{0}(\mathbb{Z}F(\unicode[STIX]{x1D6E5}_{k}^{\bullet },\mathbb{G}_{m}^{\wedge n}))=K_{n}^{MW}(k)$</jats:tex-math></jats:alternatives></jats:inline-formula>, where<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1474748016000190_inline6" /><jats:tex-math>$\mathbb{Z}F_{\ast }(k)$</jats:tex-math></jats:alternatives></jats:inline-formula>is the category of linear framed correspondences of algebraic<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1474748016000190_inline7" /><jats:tex-math>$k$</jats:tex-math></jats:alternatives></jats:inline-formula>-varieties, introduced by Garkusha and Panin [The triangulated category of linear framed motives<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1474748016000190_inline8" /><jats:tex-math>$DM_{fr}^{eff}(k)$</jats:tex-math></jats:alternatives></jats:inline-formula>, in preparation] (see [Garkusha and Panin, Framed motives of algebraic varieties (after V. Voevodsky), Preprint, 2014,<jats:uri xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="http://www.arxiv.org/abs/1409.4372">arXiv:1409.4372</jats:uri>], § 7 as well), and<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1474748016000190_inline9" /><jats:tex-math>$K_{\ast }^{MW}(k)$</jats:tex-math></jats:alternatives></jats:inline-formula>is the Milnor–Witt<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1474748016000190_inline10" /><jats:tex-math>$K$</jats:tex-math></jats:alternatives></jats:inline-formula>-theory of the base field<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1474748016000190_inline11" /><jats:tex-math>$k$</jats:tex-math></jats:alternatives></jats:inline-formula>.</jats:p>