The triangulated category of K-motives. Issue 1 (12th May 2014) - Garkusha, Grigory; Panin, Ivan
Abstract For any perfect field k a triangulated category of K-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 k-variety X the K-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 where pt = Spec(k) and K(X) is Quillen's K-theory of X.