Oberwolfach Reports

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Volume 13, Issue 2, 2016, pp. 1753–1807
DOI: 10.4171/OWR/2016/31

Published online: 2017-02-07

Algebraic K-theory and Motivic Cohomology

Thomas Geisser[1], Annette Huber-Klawitter[2], Uwe Jannsen[3] and Marc Levine[4]

(1) Rikkyo University, Tokyo, Japan
(2) Universität Freiburg, Germany
(3) Universität Regensburg, Germany
(4) Universität Duisburg-Essen, Germany

Algebraic $K$-theory and motivic cohomology have developed together over the last thirty years. Both of these theories rely on a mix of algebraic geometry and homotopy theory for their construction and development, and both have had particularly fruitful applications to problems of algebraic geometry, number theory and quadratic forms. The homotopy-theory aspect has been expanded significantly in recent years with the development of motivic homotopy theory and triangulated categories of motives, and $K$-theory has provided a guiding light for the development of non-homotopy invariant theories. 19 one-hour talks presented a wide range of latest results on many aspects of the theory and its applications.

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Geisser Thomas, Huber-Klawitter Annette, Jannsen Uwe, Levine Marc: Algebraic K-theory and Motivic Cohomology. Oberwolfach Rep. 13 (2016), 1753-1807. doi: 10.4171/OWR/2016/31