The triangulated category of K-motives. Issue 1 (12th May 2014)

• Record Type: Journal Article
• Authors: Garkusha, Grigory; Panin, Ivan
• Is Part Of: Journal of K-Theory. Volume 14:Issue 1(2014)
• Page Start: 103
• Page End: 137
• Publication Date: 2014-05-12
• Subjects: K-theory -- Periodicals; 512.6605
• DOI: 10.1017/is014004013jkt263
• Languages: English
• ISSNs: 1865-2433

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>For any perfect field <italic>k</italic> a triangulated category of <italic>K</italic>-motives <inline-graphic xlink:href="ark:/27927/pghw30g04r" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> is constructed in the style of Voevodsky's construction of the category <inline-graphic xlink:href="ark:/27927/pghw30g037" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />. To each smooth <italic>k</italic>-variety <italic>X</italic> the <italic>K</italic>-motive <inline-graphic xlink:href="ark:/27927/pghw30g06s" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> is associated in the category <inline-graphic xlink:href="ark:/27927/pghw30g04r" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> and</p> <p> <disp-formula> <graphic mimetype="image" position="anchor" xlink:href="ark:/27927/pghw30g058" xlink:type="simple" orientation="portrait" xmlns:xlink="http://www.w3.org/1999/xlink" /> </disp-formula> </p> <p>where <italic>pt</italic> = Spec(<italic>k</italic>) and <italic>K(X)</italic> is Quillen's <italic>K</italic>-theory of <italic>X</italic>.</p> </abstract>