caa a22 4500 475738101 CHVBK 20180406123452.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1007/s002220050014 doi (NATIONALLICENCE)springer-10.1007/s002220050014 The K-theory of fields in characteristic p [Elektronische Daten] [Thomas Geisser, Marc Levine] Abstract. : We show that for a field k of characteristic p, H i (k,ℤ(n)) is uniquely p-divisible for i≠n (we use higher Chow groups as our definition of motivic cohomology). This implies that the natural map K n M (k)?K n (k) from Milnor K-theory to Quillen K-theory is an isomorphism up to uniquely p-divisible groups, and that K n M (k) and K n (k) are p-torsion free. As a consequence, one can calculate the K-theory mod p of smooth varieties over perfect fields of characteristic p in terms of cohomology of logarithmic de Rham Witt sheaves, for example K n (X,ℤ/p r )=0 for n>dimX. Another consequence is Gersten's conjecture with finite coefficients for smooth varieties over discrete valuation rings with residue characteristic p. As the last consequence, Bloch's cycle complexes localized at p satisfy all Beilinson-Lichtenbaum-Milne axioms for motivic complexes, except possibly the vanishing conjecture. Springer-Verlag Berlin Heidelberg, 2000 Mathematics Subject Classification (1991): 19D50, 19D45, 19E08, 14C25 nationallicence Geisser Thomas Institute for Experimental Mathematics, Ellernstr. 29, D-45326 Essen, Germany¶(e-mail: geisser@exp-math.uni-essen.de), DE aut Levine Marc Department of Mathematics, Northeastern University, Boston, MA 02115, USA¶(e-mail: marc@neu.edu), US aut https://doi.org/10.1007/s002220050014 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002220050014 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Geisser Thomas Institute for Experimental Mathematics, Ellernstr. 29, D-45326 Essen, Germany¶(e-mail: geisser@exp-math.uni-essen.de), DE aut NATIONALLICENCE 700 1- Levine Marc Department of Mathematics, Northeastern University, Boston, MA 02115, USA¶(e-mail: marc@neu.edu), US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer