This volume presents the proceedings of the Joint Summer Research Conference on Algebraic $K$-theory held at the University of Washington in Seattle. High-quality surveys are written by leading experts in the field. Included is the most up-to-date published account of Voevodsky's proof of the Milnor conjecture relating the Milnor $K$-theory of fields to Galois cohomology. This book offers a comprehensive source for cutting-edge research on the topic.

Readership

Graduate students and research mathematicians interested in $K$-theory, algebraic geometry, and number theory.

Table of Contents

• J.-L. Colliot-Thélène -- Conjectures de type local-global sur l'image des groupes de Chow dans la cohomologie étale
• H. Esnault -- Algebraic theory of characteristic classes of bundles with connection
• H. Gangl and S. Müller-Stach -- Polylogarithmic identities in cubical higher Chow groups
• T. Geisser and L. Hesselholt -- Topological cyclic homology of schemes
• H. Gillet and C. Soulé -- Filtrations on higher algebraic $K$-theory
• B. Kahn -- Motivic cohomology of smooth geometrically cellular varieties
• K. P. Knudson -- Integral homology of $PGL_2$ over elliptic curves
• E. Peyre -- Application of motivic complexes to negligible classes
• J. Rognes -- Two-primary algebraic $K$-theory of spaces and related spaces of symmetries of manifolds
• J. Rosenberg -- A mini-course on recent progress in algebraic $K$-theory and its relationship with topology and analysis
• B. Totaro -- The Chow ring of a classifying space
• V. Voevodsky -- Voevodsky's Seattle lectures: $K$-theory and motivic cohomology
• C. Weibel -- Products in higher Chow groups and motivic cohomology